Posted by **Laquisha** on Sunday, October 14, 2012 at 7:05pm.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter running track.

a) Draw a figure that visually represents the problem. Let x and y represent the length and width of the rectangular region.

b) Determine the radius of the semicircular ends of the track.

c) Use the result of part b to write an equation in terms of x and y, for the distance traveled in one lap around the track. Solve for x.

d) Use the result of part c to write the area A of the rectangular region as a function of x.

- Pre-Calculus -
**Reiny**, Sunday, October 14, 2012 at 7:44pm
length of rectangle -- x

width of rectangle --- y

b) radius of semicircle is y/2

c) distance = 2 lengths + 2 halfcircles

= 2x +2(1/2) π(y/2)^2

= 2x + π(y^2)/4

2x + (1/4)πy^2 = 200

times 4

8x + πy^2 = 800

x = (800 - πy^2)/8

d) -- poorly worded question.

Since they had you solve for x in c) they should have asked for the area in terms of y , not x

check your typing.

BTW, I would have defined the radius of the semicircle as r

then the width of the rectangle would be 2r, and we can avoid some of these nasty fractions.

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