USING STRUCTURE An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles, as shown. A drawing shows an indoor track. It is shaped like a rectangle with a semi-circle on each of the shorter sides. The length of the rectangle is labeled x. The radius of each semi-circle is labeled r. A. Write a formula for the perimeter of the indoor track. $P=$ b. Solve the formula for $x$ . $x=$ Question 2 c. The perimeter of the track is 660 feet, and $r$ is 50 feet. Find $x$ . Round your answer to the nearest foot. $x=$ feet

Step-by-step explanation:

Find the digram attached.

Perimeter of the track = perimeter of the rectangle + perimeter of the 2semicircles

Perimter of a rectangle = 2(x+r) where:

x is the length

2r is the width of the rectangle = diameter of the semicircle

Perimeter of semicircle = 2πr/2 = πr

Perimeter of 2semicirle = 2πr

Perimeter of the track = 2(x+2r) + 2πr

r is the radius if the semicircle

Expand

Perimeter of the track = 2x+4r + 2πr

Perimeter of the track = 2(x+2r+πr)

b) Given P = 2(x+2r+πr), we are to make x the subject of the formula.

P = 2x+4r+2πr

P-4r-2πr = 2x

Divide both sides by 2.

(P-4r-2πr)/2 = 2x

x = (P-4r-2πr)/2

c) Given

P = 600fr

r = 50ft

x = (600-4(50)-2π(50))/2

x = (600-200-100(3.14))/2

x = 400-314/2

x = 86/2

x = 43ft

Hence the value of x to nearest foot is 43ft