Question

An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles.

a. Write a formula for the perimeter of the indoor track
P=

b. Solve the formula for x.
x=

c. The perimeter of the track is 660 feet, and r is 50 feet. Find x. Round to the nearest foot.
x=____feet
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Answer 1

(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)

Ok, we have a rectangle of length x by r.

At the extremes of length r, we add two semicircles.

So the perimeter will be equal to:

Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).

The radius of the semicircles is r, and the perimeter of a circle is:

C = 2*pi*r

where pi = 3.14

Then the perimeter of the track is:

P = 2*x + 2*pi*r.

b) now we want to solve this for x, this means isolating x in one side of the equation.

P - 2*pi*r = 2*x

P/2 - pi*r = x.

c) now we have:

P = 660ft

r = 50ft

then we can replace the values and find x.

x = 660ft/2 - 3.14*50ft = 173ft