Tutors Answer Your Questions about Geometry Word Problems (FREE)
Question 1207480: If a polygon of n sides has (1/2)(n)(n - 3) diagonals, how many sides will a polygon with 65 diagonals have? Is there a polygon with 80 diagonals?
Let me see.
I understand this problem leading to this equation:
(n/2)(n - 3) = 65
I then set up another equation to look like this:
(n/2)(n - 3) = 80
I now need to solve each equation for n.
Yes?
Click here to see answer by ikleyn(52781)   |
Question 1207480: If a polygon of n sides has (1/2)(n)(n - 3) diagonals, how many sides will a polygon with 65 diagonals have? Is there a polygon with 80 diagonals?
Let me see.
I understand this problem leading to this equation:
(n/2)(n - 3) = 65
I then set up another equation to look like this:
(n/2)(n - 3) = 80
I now need to solve each equation for n.
Yes?
Click here to see answer by math_tutor2020(3817) |
Question 1207536: Evelyn is thinking of constructing a rectangular shaped swimming pool in the plot next to her house such that it is surrounded by grass. The dimensions of the plot is 50 ft × 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
Click here to see answer by josgarithmetic(39617) |
Question 1207536: Evelyn is thinking of constructing a rectangular shaped swimming pool in the plot next to her house such that it is surrounded by grass. The dimensions of the plot is 50 ft × 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
Click here to see answer by mananth(16946)  |
Question 1207536: Evelyn is thinking of constructing a rectangular shaped swimming pool in the plot next to her house such that it is surrounded by grass. The dimensions of the plot is 50 ft × 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
Click here to see answer by greenestamps(13200)  |
Question 1207601: An open box is to be constructed from a square 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 5 cubic feet, what should be the dimension of the sheet metal?
Note: This is a popular problem found in many textbooks but I haven't found one decent explanation. Can someone solve this application one step at a time?
Click here to see answer by ikleyn(52781) |
Question 1207601: An open box is to be constructed from a square 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 5 cubic feet, what should be the dimension of the sheet metal?
Note: This is a popular problem found in many textbooks but I haven't found one decent explanation. Can someone solve this application one step at a time?
Click here to see answer by Theo(13342)  |
Question 1207601: An open box is to be constructed from a square 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 5 cubic feet, what should be the dimension of the sheet metal?
Note: This is a popular problem found in many textbooks but I haven't found one decent explanation. Can someone solve this application one step at a time?
Click here to see answer by MathTherapy(10552)  |
Question 1207752: 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 mananth(16946) |
Question 1207752: 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(52781) |
Question 1207769: 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 = 2(pi)(r^2) + 2(pi)rh, where r is the radius and h is the height.
I say the set up I'd this:
188.5 = 2(pi)(r^2) + 2(pi)7r
I now must find r.
Yes?
Click here to see answer by mananth(16946) |
Question 1207769: 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 = 2(pi)(r^2) + 2(pi)rh, where r is the radius and h is the height.
I say the set up I'd this:
188.5 = 2(pi)(r^2) + 2(pi)7r
I now must find r.
Yes?
Click here to see answer by math_tutor2020(3817) |
Question 1207769: 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 = 2(pi)(r^2) + 2(pi)rh, where r is the radius and h is the height.
I say the set up I'd this:
188.5 = 2(pi)(r^2) + 2(pi)7r
I now must find r.
Yes?
Click here to see answer by ikleyn(52781) |
Question 1207821: An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting.
(a) If the painting is square, what are its dimensions? What are the dimensions of the frame?
(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?
Click here to see answer by greenestamps(13200) |
Question 1207821: An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting.
(a) If the painting is square, what are its dimensions? What are the dimensions of the frame?
(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?
Click here to see answer by ikleyn(52781) |
Question 1207821: An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting.
(a) If the painting is square, what are its dimensions? What are the dimensions of the frame?
(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?
Click here to see answer by mananth(16946) |
Question 1207822: One formula stating the relationship between the length l and width of a rectangle of “pleasing proportion”is w L^2 = w(L + w). How should a 4 foot by 8 foot sheet of plasterboard be cut so that the result is a rectangle of “pleasing proportion” with a width of 4 feet?
Click here to see answer by ikleyn(52781) |
Question 1207840: The vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5).
(a) Find the perimeter of triangle ABC.
(b) Find the perimeter of the triangle that is formed by joining the midpoints of the three sides of triangle ABC.
(c) Compute the ratio of the perimeter in part (a) to the perimeter in part (b).
(d) What theorem from geometry provides the answer for part (c) without using the results in (a) and (b)?
Click here to see answer by mananth(16946) |
Question 1207910: The original Ferris wheel was built in 1893 by Pittsburgh,Pennsylvania,bridge builder George W.Ferris. The Ferris wheel was originally built for the 1893 World’s Fair in Chicago,but was also later reconstructed for the 1904 World’s Fair in St. Louis. It had a maximum height of 264 feet and a wheel diameter of 250 feet. Find an equation for the wheel if the center of the wheel is on the y-axis.
Click here to see answer by ikleyn(52781) |
Question 1207911: Earth is represented on a map of a portion of the solar system so that its surface is the circle with equation x^2 + y^2 + 2x + 4y - 4091 = 0. A weather satellite circles 0.6 unit above Earth with the center of its circular orbit at the center of Earth. Find the equation for the orbit of the satellite on this map.
Click here to see answer by math_tutor2020(3817) |
Question 1207916: Find the area of the blue shaded region in the picture, assuming the quadrilateral inside the circle is a square.
Note:
1. There is a square inside a circle.
2. The square is not shaded.
3. The circle is shaded blue.
4. The equation of the circle given is x^2 + y^2 = 36.
Click here to see answer by mananth(16946) |
Question 1207915: In 2008, the Singapore Flyer opened as the world’s largest Ferris wheel. It has a maximum height of 165 meters and a diameter of 150 meters,with one full rotation taking approximately 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis.
Click here to see answer by ikleyn(52781) |
Question 1208031: The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x) = 4x•sqrt{1 - x^2} where x represents the length,in feet, of half the base of the beam. Determine the cross-sectional area of the beam if the length of half the base of the beam is One-third of a foot
Click here to see answer by mananth(16946) |
Question 1208248: Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister's house
partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen's average speed
was four miles per hour faster than Anne's. Find Helen's average speed and Anne's average speed.
Click here to see answer by josgarithmetic(39617) |
Question 1208248: Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister's house
partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen's average speed
was four miles per hour faster than Anne's. Find Helen's average speed and Anne's average speed.
Click here to see answer by timofer(104) |
Question 1208248: Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister's house
partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen's average speed
was four miles per hour faster than Anne's. Find Helen's average speed and Anne's average speed.
Click here to see answer by MathTherapy(10552) |
Question 1208412: A circular swimming pool, 25 feet in diameter, is enclosed by a deck that is 5 feet wide. What is the area of the deck? How much fence is required to enclose the deck?
Let me see. I understand this scenario to be one circle inside another circle. The circle inside is the pool, and the circle surrounding the pool is the deck.
To find the area of the deck, I must subtract the area of the pool from the area of the deck.
Yes?
To find how much fencing is required to enclose the deck, I must find the circumference of the deck.
Yes?
Click here to see answer by ikleyn(52781) |
Question 1208415: A person who is 6 feet tall is standing on the beach in Florida and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?
A friend told me to use the following facts and formula.
d = distance the ship is from shore
r = radius of Earth = 3960 miles
m = number of feet in a mile = 5280
h = height of the person standing on the beach in Florida
d^2 + r^2 = [(r + (h/m)]^2
We want d.
d^2 + (3960)^2 = [(3960) + (6/5280)]^2
Is my friend correct?
Click here to see answer by ikleyn(52781) |
Question 1208411: A Norman window consists of a rectangular shape surmounted by a semicircle. The length of the rectangle is 16 feet, and the width is 14 feet. Find the area of the Norman window. How much wood frame is needed to enclose the window?
Let me see.
To find the area of Norman window, I must add the area of the semicircle and the area of the rectangle.
You say?
To find how much wood frame is needed to enclose the window, I can use the formula C = pi•r, where C is the circumference of the semicircle and r is the radius of the semicircle
You day?
Click here to see answer by timofer(104) |
Question 1208483: until this year greenville has averaged 25.68 inches of rainfall per year for more than a century this year's rainfall showed a changed of -2 3/8% with respect to the previous average how much rain fall this year
Click here to see answer by ikleyn(52781) |
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