# Questions on Geometry: Geometric formulas answered by real tutors!

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 Geometric and Other Formulas Answers archive In Depth

 Question 281785: Choose the most efficient strategy for solving the following problem: A group of surveyors left their base camp and traveled 50 km east, then 20 km north, then 10 km west, then 50 km south. How far were they from their base camp? a. look for a pattern b. draw a diagram c. work backward d. make a chart Next question is to solve this problem. a. 50km b. 130km c. 92 km d. they were back at their base camp. Click here to see answer by richwmiller(9135)

 Question 285620: Ray SU bisects angle RST. The measure of angle RSU=6x-3 and the measure of angle UST=5x+4. Find the measure of RSU. Click here to see answer by Alan3354(30993)

 Question 285624: if the radius of a circle is tripled, the diameter is also tripled. true or false? I think it is true Click here to see answer by Alan3354(30993)
 Question 285624: if the radius of a circle is tripled, the diameter is also tripled. true or false? I think it is true Click here to see answer by richwmiller(9135)

 Question 286202: if there is an right angle and a side is 15 while b side is 25 how can i get da value of x for c Click here to see answer by richwmiller(9135)

 Question 286543: Given F(X)=x-3 and g(X)= X^2 over x-3 find g(f(x)) Click here to see answer by jim_thompson5910(28593)

 Question 287297: Will you please help with this problem with great detail. Thank You One side of an equilateral triangle is four yards less than the side of a square. The perimeter of the triangle is twenty-eight yards shorter than the perimeter of the square. Find the length of the sides of the triangle and square. Click here to see answer by richwmiller(9135)

 Question 290078: How do you solve- A squared + 15 = 2A squared - 65? Click here to see answer by dabanfield(803)

 Question 292469: A boy standing on the shore of a lake 1 mile wide wants to go to the store 3 miles down the shore on the opposite side of the lake. If he swims at 2 miles per hour, and walks at 4 miles per hour, is it quicker for him to swim directly across the lake and then walk to the store, or is it quicker for him to swim directly to the store? Prove this mathematically. Click here to see answer by richwmiller(9135)
 Question 292469: A boy standing on the shore of a lake 1 mile wide wants to go to the store 3 miles down the shore on the opposite side of the lake. If he swims at 2 miles per hour, and walks at 4 miles per hour, is it quicker for him to swim directly across the lake and then walk to the store, or is it quicker for him to swim directly to the store? Prove this mathematically. Click here to see answer by Alan3354(30993)

 Question 293434: A clay model of an automobile is 8 inches and weighs 2 pounds, what would a full-size model weigh if it were 12 feet? Click here to see answer by unlockmath(1599)

 Question 294004: what is X??? X2(squared)+ 1 = 8x - 14 Click here to see answer by checkley77(12569)

 Question 295422: What is the geometric mean for the numbers 175 and 7? Click here to see answer by stanbon(57314)

 Question 295434: The unit of measure for a line is in inches. Use the distance formula to find the length of the line with points at (-3,0) and (4,3). Click here to see answer by Alan3354(30993)

 Question 295610: State the ordered pair that satisfies the equation 2x-5y= -1. a) (2, 4/5) b) (0. 3/5) c) (1, 4/5) d) (1, 3/5) Click here to see answer by richwmiller(9135)

 Question 295612: Find the ordered pair that is a solution to this system of inequalities y>x+1 y>-x +3 a) y>2,3 b) y> 1,2 c) y> 4,5 d) y> 5,6 Click here to see answer by stanbon(57314)

 Question 295982: If a tv screen measures 56" diagnal and 49" across the bottom what is the height of the tv screen. Click here to see answer by nerdybill(6958)

 Question 297848: An inflated beach ball with radius r=25 centimeters hold approximately 65.400 cubic centimeters of air. When the ball is compressed, the radius is 2/3 the original size. Approximately how much air does the partially deflated ball now hold? Click here to see answer by Alan3354(30993)

 Question 300737: I need major help on how to answer these questions and what they are. Here is the info... * The slash / represents a fraction bar and division. For example, one half = 1/2. * The notation sqrt( ) is used to denote the square root of a number. To answer some of the following questions you will need to refer to the figures below: Figure 1: The three horizontal lines are parallel. Figure 3: The two horizontal lines are parallel. Figure 7: JM and JP are chords of the circle. JK is a diameter. Figure 8: GH and JK are chords of the circle. Use Figure 3 below for the following proof: Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°. Prove: lines a and b are parallel. 1. m ang 1 + m ang 3 = 180o : Given 2. m ang 3 + m ang 5 = 180° : Definition of straight angle 3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________ 4. m ang 1 = m ang 5 : __________ 5. Lines a and b are parallel: __________ Here are the figures that go with the questions: http://i44.tinypic.com/s153m1.png And here are the questions: 11.) Find the measure of the supplement of the angle with measure 85 degrees. 5 degrees 105 degrees 95 degrees 58 degrees 12.) If CG is an altitude of Triangle ABC, then _______. CG is perpendicular to AB CA is perpendicular to AB G is the midpoint of AB CG is parallel to BC 13.) What is the equation of the line through points (-3, 2) and (-4, 5)? y = (2/3)x - 6 y = 2x - 4 y = 2x + 2 y = -3x - 7 14.) Given Triangle RST is similar to Triangle DEF. If m Ang E = 38°, m Ang R = 43°, and m Ang T = (7x + 8)°, then x = ? 13 14.14 4.29 15 15.) With only a compass and a straightedge it is possible to construct a square. True False Neither Both 16.) If the sides of one angle are opposite rays of the sides of another angle, then the two angles are vertical angles. True False Neither Both 17.) In Figure 7, if m Ang PJK = 37° and m Arc PM = 41°, then m Ang MJK = 16.5° 9° 33° 12° 18.) If two polygons are similar, then they are congruent. True False Neither Both 19.) Use Figure 1 above. If m Ang 1 = 30°, then m Ang 11 = _______. 30° 60° 120° 150° 20.) A trapezoid of area 150 square units has one base of length 18 and height 12. Find the length of the other base C 3.5 7 3 sqrt(2) 14 21.) Refer to triangle DEF in Figure 5, if m Ang D = 30o, m Ang E = 60°, and DF = 12, what is ME in simplest form? 2 sqrt(3) 6 6 sqrt(3) 12 :( this is an ungraded study guide but counted as an incomplete if not done. please help? :( I don't understand how to do this. Click here to see answer by Fombitz(13828)

 Question 300741: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info... * The slash / represents a fraction bar and division. For example, one half = 1/2. * The notation sqrt( ) is used to denote the square root of a number. To answer some of the following questions you will need to refer to the figures below: Figure 1: The three horizontal lines are parallel. Figure 3: The two horizontal lines are parallel. Figure 7: JM and JP are chords of the circle. JK is a diameter. Figure 8: GH and JK are chords of the circle. Use Figure 3 below for the following proof: Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°. Prove: lines a and b are parallel. 1. m ang 1 + m ang 3 = 180o : Given 2. m ang 3 + m ang 5 = 180° : Definition of straight angle 3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________ 4. m ang 1 = m ang 5 : __________ 5. Lines a and b are parallel: __________ Here are the figures that go with the questions: http://i44.tinypic.com/s153m1.png And here are the questions: 42.) In the proof above, the reason for step 4 is substitution angle addition equal corresponding angles parallel postulate 43.) For Figure 4, find DE. 6 8 10 12 44.) If two triangles are congruent, then the _______ corresponding parts are congruent. 3 6 4 2 45.) Lines p and q are parallel. The slope of p is 5 and the slope of q is 10/v. What is v? 2 sqrt(13) 4 4 sqrt(2) 2 46.) For Figure 6, 0A = 3 and AC = 12, what is OB? 3sqrt(9) 3 sqrt(3) 7 sqrt(153) 47.) Classify the angle with measure 75 degrees. Acute Obtuse Straight Right 48.) A parallelogram of area 78 square units has one side of length 12. Find the length of an altitude to that side. 3 2 sqrt(3) 6 6.5 49.) Refer to Triangle DFE in Figure 5, if DM = 4 and ME = 8, what is FM in simplified form? 4 sqrt(2) 12 2 sqrt(3) 16 50.) In elliptic or spherical geometry, there can be _____ right angle(s) in a triangle. zero one two three 51.) For right triangle ACB with right angle C, if m Ang A = 45° and BC = 3, what is the length of AC? 3 sqrt(3) 3 3 sqrt(2) 1.5 52.) Opposites sides of a parallelogram are parallel and congruent. True False Neither Both 53.) In the proof above, the reason for step 3 is substitution angle addition parallel postulate equal corresponding angles Click here to see answer by Fombitz(13828)

 Question 300740: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info... * The slash / represents a fraction bar and division. For example, one half = 1/2. * The notation sqrt( ) is used to denote the square root of a number. To answer some of the following questions you will need to refer to the figures below: Figure 1: The three horizontal lines are parallel. Figure 3: The two horizontal lines are parallel. Figure 7: JM and JP are chords of the circle. JK is a diameter. Figure 8: GH and JK are chords of the circle. Use Figure 3 below for the following proof: Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°. Prove: lines a and b are parallel. 1. m ang 1 + m ang 3 = 180o : Given 2. m ang 3 + m ang 5 = 180° : Definition of straight angle 3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________ 4. m ang 1 = m ang 5 : __________ 5. Lines a and b are parallel: __________ Here are the figures that go with the questions: http://i44.tinypic.com/s153m1.png And here are the questions: 31.) At five o'clock the measure of the angle formed by the hands of the clock is? 60° 210° 150° 180° 32.) In angle ABC, A is the vertex. True False Neither Both 33.) A regular polyhedron is a polyhedron with faces that are congruent squares. True False Neither Both 34.) In Figure 7 if m Arc PM = 40° and m Arc JKM = 210°, then m Ang PJK = 70° 35° 55° 40° 35.) If a triangle has sides of lengths 8, 4, and 4 sqrt(3), is the triangle right? Yes No Maybe Sometimes 36.) A triangle with at least two sides of equal length is called _______. Scalene Isosceles Equilateral Regular 37.) A polygon is regular if and only if the sides are congruent (“if and only if” states a condition but does not necessitate it to be the sole condition). False True Neither Both 38.) In the proof above, the reason for step 5 is substitution parallel postulate equal corresponding angles angle addition 39.) What is the center of the circle with equation (x + 1)^2 + (y + 3)^2 = 9/4? (-1, -3) (-1, -1) (-3/2, 4) (1, 3) 40.) Use Figure 2 above. If m Ang B = 53° and m Ang C = 62°, which side(s) of Triangle ABC is(are) the longest? AB BC AC AB & BC 41.) What is the equation of the line with slope 2/3 and passes through the midpoint of the segment joining points (-1, 6) and (-7, -4)? y = -3x - 9 y = (2/3)x + (11/3) y = -3x - 7 y = (2/3)x - 6 Click here to see answer by Fombitz(13828)

 Question 300738: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info... * The slash / represents a fraction bar and division. For example, one half = 1/2. * The notation sqrt( ) is used to denote the square root of a number. To answer some of the following questions you will need to refer to the figures below: Figure 1: The three horizontal lines are parallel. Figure 3: The two horizontal lines are parallel. Figure 7: JM and JP are chords of the circle. JK is a diameter. Figure 8: GH and JK are chords of the circle. Use Figure 3 below for the following proof: Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°. Prove: lines a and b are parallel. 1. m ang 1 + m ang 3 = 180o : Given 2. m ang 3 + m ang 5 = 180° : Definition of straight angle 3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________ 4. m ang 1 = m ang 5 : __________ 5. Lines a and b are parallel: __________ Here are the figures that go with the questions: http://i44.tinypic.com/s153m1.png And here are the questions: 22.) A square has diagonals of length 8 cm. Find the area. ___ square cm 32 16 sqrt(2) 12 3 sqrt(2) 23.) the measure of the complement of the angle with measure 45 degrees. 315 degrees 45 degrees 55 degrees 135 degrees 24.) Use Figure 1. The exterior angles of Angle 3 are _______. Angles 1 and 2 Angles 5, 6, and 7 Angles 2 and 4 Angles 1, 2, and 4 25.) In Figure 8, if GI = 3, IH = 8, JK = 10, what is JI (if it is longer than IK)? 8 12 6 4 26.) All opposite sides of a trapezoid are parallel. True False Neither Both 27.) What is the volume of a right cone with radius 3 and height 4? ___ (pi) cubic units 16 24 12 27 28.) For Figure 4, find AC. 26 2/3 9.5999999999999996447286321199499070644378662109375 10 15 29.) The converse of the statement: "If you are baking brownies, then the kitchen smells good", is "If the kitchen smells good, then you are baking brownies." True False Neither Both 30.) The radius of a Circle O is 4, if radii OA and OB form 90° angle, AB = ? 4 sqrt(2) 4 16 sqrt(2) 8 Click here to see answer by Fombitz(13828)

 Question 300736: I need major help on how to answer these questions and what they are. Here is the info... * The slash / represents a fraction bar and division. For example, one half = 1/2. * The notation sqrt( ) is used to denote the square root of a number. To answer some of the following questions you will need to refer to the figures below: Figure 1: The three horizontal lines are parallel. Figure 3: The two horizontal lines are parallel. Figure 7: JM and JP are chords of the circle. JK is a diameter. Figure 8: GH and JK are chords of the circle. Use Figure 3 below for the following proof: Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°. Prove: lines a and b are parallel. 1. m ang 1 + m ang 3 = 180o : Given 2. m ang 3 + m ang 5 = 180° : Definition of straight angle 3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________ 4. m ang 1 = m ang 5 : __________ 5. Lines a and b are parallel: __________ Here are the figures that go with some of the questions: http://i44.tinypic.com/s153m1.png And here are the questions: The point where the three altitudes of a triangle intersect is called the intersection point altocenter centroid orthocenter 2.) Classify the angle with measure 180 degrees. Acute Obtuse Straight Right 3.) In Figure 8, if GH = 8, JI = 8, IK = 2, what is GI? 8 4 6 10 4.) If we wanted to draw a median of Triangle ABC coming from vertex C, then our line would _______. cross BC at its midpoint cross AB at its midpoint cross and be perpendicular to BC cross and be perpendicular to AB 5.) The base of a pyramid is a square with sides of length 4 cm. If the volume = 80 cm3, what is the height? ___ cm 16 / 3 12 15 5 sqrt(3) / 3 6.) Find the value of x: (2x) / 7 = (x - 1) / 3 1 13/7 7 5/7 7.) A line that intersects a circle in a single point. chord secant tangent diameter 8.) A circle of area 49(pi) has a circumference of what? 7 pi 17.5 10 14 pi 9.) If two sides and the _______ angle of one triangle are congruent to two sides and the _______ angle of another triangle, then the triangles are congruent. Smallest Opposite Included Acute 10.) When constructing the median of a triangle, it is possible that the median may lie exterior to the triangle. True False Neither Both Thank you so much! :( this is just a study guide (ungraded but counted as an incomplete if not done. Click here to see answer by Fombitz(13828)

 Question 301113: The area of a square garedn is 242 m^2. How long is the diagonal? Click here to see answer by mananth(12270)
 Question 301113: The area of a square garedn is 242 m^2. How long is the diagonal? Click here to see answer by nyc_function(2733)

 Question 301463: If you double the length and the height and the width of a room, what does that do to the volume? Click here to see answer by checkley77(12569)

 Question 301960: One side of a triangle is 2 cm shorter than the base. The other side is 3 cm longer than the base. What lengths of the base will allow the perimeter to be greater than 19 cm?” Click here to see answer by london maths tutor(243)

 Question 302446: what is the geometric mean of x and 96 is 24. what is x? Click here to see answer by jim_thompson5910(28593)

 Question 302936: what is the area of a regular hexagon with the side length of 4cm Click here to see answer by Alan3354(30993)

 Question 302935: what is the area of a regular pentagon with the perimeter of 50cm Click here to see answer by Alan3354(30993)

 Question 304426: what is the height of a cyliner that has a volume of 5024 and the diameter of 16 Click here to see answer by mananth(12270)

 Question 305983: Please help me to solve this problem: find the missing lengths of the triangle: 2x+1(hypotenuse), 2x-1, x .I know that the pythagorean theorem is a^2+b^2=c^2 I keep getting x=0, but I know it's not the right answer. Click here to see answer by checkley77(12569)

 Question 306293: Please help. My son is having a terrible time in geometry and I never took it so I'm of no help. Given: the angle of BCA = 50 degrees. The arc of CD = 80 degrees How do I find the arc of AD? (in layterms please) Thanks so much for any help you can offer. Click here to see answer by Alan3354(30993)

 Question 306617: Sorry for the lact of picture...I don't know how to post it. I do know that it is an oblique triangle where a is the bottom (width) and b and c are on the left and right side, respectively. a = 5, b = 6, and angle between a and b = 1/3pi. Find c. Thank you in advance. Click here to see answer by stanbon(57314)

 Question 306683: Write an equation and solve for x if the area of the rectangle is 55 square units. the length of a side is 3x-1 and the height is 5 Click here to see answer by mananth(12270)

 Question 306911: What is the value of x if 54 times the square root of 3 equals x cubed? Click here to see answer by checkley77(12569)

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