Tutors Answer Your Questions about Geometry Word Problems (FREE)
Question 1208717: How many right triangles have a hypotenuse that measures 2x + 3 meters and legs that measure 2x - 5 meters and x + 7 meters? What are the dimensions of the triangle(s)?
I am thinking Pythagorean Theorem.
My setup:
(2x - 5)^2 + (x + 7)^2 = (2x + 3)^2
You say?
Click here to see answer by ikleyn(52778)   |
Question 1208718: Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters.
For this problem, I must use the perimeter of a rectangle formula and area of a rectangle formula. Do you agree?
Let l = length
Let w = width
A = lw
40 = lw
I can solve the equation for length or width. I will solve for l or length.
40 = lw
40/w = l
I now plug that into the formula
P = 2l + 2w
26 = 2(40/w) + 2w
After finding w or width, I plug the value for w back into A = lw to find the length.
Is this correct? If not, what did I fo wrong? Thanks.
Click here to see answer by josgarithmetic(39617) |
Question 1208718: Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters.
For this problem, I must use the perimeter of a rectangle formula and area of a rectangle formula. Do you agree?
Let l = length
Let w = width
A = lw
40 = lw
I can solve the equation for length or width. I will solve for l or length.
40 = lw
40/w = l
I now plug that into the formula
P = 2l + 2w
26 = 2(40/w) + 2w
After finding w or width, I plug the value for w back into A = lw to find the length.
Is this correct? If not, what did I fo wrong? Thanks.
Click here to see answer by MathTherapy(10552)  |
Question 1208718: Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters.
For this problem, I must use the perimeter of a rectangle formula and area of a rectangle formula. Do you agree?
Let l = length
Let w = width
A = lw
40 = lw
I can solve the equation for length or width. I will solve for l or length.
40 = lw
40/w = l
I now plug that into the formula
P = 2l + 2w
26 = 2(40/w) + 2w
After finding w or width, I plug the value for w back into A = lw to find the length.
Is this correct? If not, what did I fo wrong? Thanks.
Click here to see answer by greenestamps(13200)  |
Question 1208729: An open box is to be constructed from a piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should the dimensions of the sheet metal be?
Let me see.
I see the word volume. The problem talks about a box.
I need the volume of a rectangular box formula.
V = length x width x height
or V = lwh for short.
Length = x - 24
Width = x - 24
Height is 12.
My setup is as follows:
Let x = dimensions of the sheet metal
V = (x - 24)(x - 24)(12)
Is my volume setup correct?
Click here to see answer by timofer(104) |
Question 1208729: An open box is to be constructed from a piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should the dimensions of the sheet metal be?
Let me see.
I see the word volume. The problem talks about a box.
I need the volume of a rectangular box formula.
V = length x width x height
or V = lwh for short.
Length = x - 24
Width = x - 24
Height is 12.
My setup is as follows:
Let x = dimensions of the sheet metal
V = (x - 24)(x - 24)(12)
Is my volume setup correct?
Click here to see answer by greenestamps(13200) |
Question 1208729: An open box is to be constructed from a piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should the dimensions of the sheet metal be?
Let me see.
I see the word volume. The problem talks about a box.
I need the volume of a rectangular box formula.
V = length x width x height
or V = lwh for short.
Length = x - 24
Width = x - 24
Height is 12.
My setup is as follows:
Let x = dimensions of the sheet metal
V = (x - 24)(x - 24)(12)
Is my volume setup correct?
Click here to see answer by ikleyn(52778) |
Question 1208737: A jumbo chocolate bar with a rectangular shape measures 12cm in length, 7cm in width, and 3cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?
Let me see.
I need V = length x width x height
Let height = thickness of bar
Length = (12 - x)
Width = (7 - x)
Height = thickness = 3cm
My setup:
V = (12 - x)(7 - x)(3)
You say?
Click here to see answer by josgarithmetic(39617) |
Question 1208737: A jumbo chocolate bar with a rectangular shape measures 12cm in length, 7cm in width, and 3cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?
Let me see.
I need V = length x width x height
Let height = thickness of bar
Length = (12 - x)
Width = (7 - x)
Height = thickness = 3cm
My setup:
V = (12 - x)(7 - x)(3)
You say?
Click here to see answer by ikleyn(52778) |
Question 1208738: A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches. How wide should the border be?
Note: 1 cubic yard = 27 cubic feet
Let me see.
I need A = πr^2.
I need the area of the pool.
A = π(5)^2
A = 25π ft^2
I need to find the total area including the border.
A = π(x + 5)^2
A = π(x^2 + 10x + 25)
A πx^2 + 10πx + 25π ft^2
Area of border = volume ÷ depth.
The depth is given in inches. I must concert to feet.
Let me see
3 inches of a foot = 3/12 = 1/4 feet.
Area of border = 27 feet ÷ (1/4) feet
Area of border = 108 feet^2.
Stuck here....
You say?
Click here to see answer by math_tutor2020(3816) |
Question 1208739: A landscaper, who just completed a rectangular flodwer garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide should the border be?
Note: 1 cubic yard = 27 cubic feet
Let me see.
Area of just the border = (2x + 6)(2x+ 10) - area of garden.
Let x = width of border in feet
Area of the border = [(2x + 6)(2x + 10) - 60]
I must convert 3 inches to feet.
3 inches ÷ 12 inches = 1/4 feet
Volume = 27 cubic feet
27 = (2x + 6)(2x + 10)(1/4)
Stuck here....
Click here to see answer by josgarithmetic(39617) |
Question 1208739: A landscaper, who just completed a rectangular flodwer garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide should the border be?
Note: 1 cubic yard = 27 cubic feet
Let me see.
Area of just the border = (2x + 6)(2x+ 10) - area of garden.
Let x = width of border in feet
Area of the border = [(2x + 6)(2x + 10) - 60]
I must convert 3 inches to feet.
3 inches ÷ 12 inches = 1/4 feet
Volume = 27 cubic feet
27 = (2x + 6)(2x + 10)(1/4)
Stuck here....
Click here to see answer by timofer(104) |
Question 1208776: The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in a 4:3 format, meaning the ratio of the length to the width of the screen is 4 to 3.
A. What is the area of a 37-inch traditional TV screen?
B. What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format?
Hint given in textbook:
If x is the length of a 4 : 3 format screen, then (3/4)(x) is the width.
Click here to see answer by math_tutor2020(3816) |
Question 1208967:
A pond is enclosed by a wooden deck that is 3 feet wide.The fence surrounding the deck is 100 feet long.
(a) If the pond is square, what are its dimensions?
(b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?
(c) If the pond is circular, what is its diameter?
(d) Which pond has the most area?
Click here to see answer by ikleyn(52778) |
Question 1209000:
A 39-ounce can of Hills Bros. coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius?
[Hint: The surface area S of a right cylinder is S = 2pi•r2 + 2pi•rh, where r is the radius, and h is the height.]
Click here to see answer by ikleyn(52778) |
Question 1209078: A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon heads east at an average speed of 40 miles per hour, while the truck heads south at an average speed of 50 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.
Click here to see answer by math_tutor2020(3816) |
Question 1209077: When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side.
A. Find an estimate for the desired intersection point.
B. Find the length of the median for the midpoint found in part A.
C. Show this error triangle on the xy-plane.
Click here to see answer by ikleyn(52778) |
Question 1209076: A hot-air balloon, headed due east at an average speed of 25 miles per hour and at a constant altitude of 125 feet, passes over an intersection. Find the expression for the distance d (measured in feet) from the balloon to the intersection t seconds later.
Click here to see answer by ikleyn(52778) |
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