SOLUTION: I need help solving this word problem: A college is building a track in the shape of a rectangle with a semicircle at each end. The perimeter of the entire track is 200 pi feet and

Question 779431: I need help solving this word problem: A college is building a track in the shape of a rectangle with a semicircle at each end. The perimeter of the entire track is 200 pi feet and the area of only the rectangular region is 5000 pi square feet. Find the length and width of the rectangular region.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

rectangle with sides and with a semicircle at each end tells you that diameter of a semicircle is equal to the one side of the rectangle; let it be side
then the radius of a semicircle is
The perimeter of the entire track is the perimeter of 2 semicircles plus two sides of the rectangle (we do not need diameters or sides , they are inside a track).
since they are congruent, the perimeter of 2 semicircle equal to the perimeter of a circle which is or since
then
......equation 1
the area of only the rectangular region is
......equation 2
solve this system:
......equation 1
......equation 2....solve for
____________________________

......equation 2.....plug in equation 1

......equation 1...solve for and cancel

.....multiply by

..........now we know radius

the width of the rectangular region is
the length of the rectangular region will be

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