Can someone help me set up an equation for the problem?
A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall. How long should the PVC plumbing pipe be?
What is the shape of the teepee? A pyramid with a square base? Most teepees I have seen are conical.
a^2+b^2=c^2
12divided by 1/2=6x6=36
8x8=64
36+64=100^2=10 ft
To set up an equation for this problem, we need to consider the shape of the teepee and the dimensions given. The teepee is essentially a triangular prism with a regular polygon as its base, which is a hexagon in this case (since it has 12 feet across).
Now, let's break down the problem step by step to set up the equation.
First, consider the base of the teepee, which is a regular hexagon. To find the length of each side of the hexagon, we divide the total circumference by the number of sides (6 sides for a hexagon). The circumference of the hexagon is equal to the length of the PVC pipe needed.
Circumference = 12 feet
Now, find the length of each side of the hexagon by dividing the circumference by 6.
Length of each side = 12 feet / 6 = 2 feet
Since the teepee is 8 feet tall, we also need to consider the height of the triangle (which is half the height of the teepee).
Height of the triangle = 8 feet / 2 = 4 feet
The length of the PVC pipe needed is equal to the slant height of the triangle. We can use the Pythagorean theorem to calculate it. The slant height is the hypotenuse of a right triangle with one leg being the height of the triangle and the other leg being half the length of the sides of the hexagon.
Using the Pythagorean theorem:
Slant height^2 = Height^2 + (Length of each side / 2)^2
Slant height^2 = 4^2 + (2/2)^2
Slant height^2 = 16 + 1
Slant height^2 = 17
Taking the square root of both sides:
Slant height = √17
Therefore, the length of the PVC plumbing pipe needed to make the teepee is approximately √17 feet.