SOLUTION: Dimensions that will produce a rectangular area of 100 Pi from a 300 meter track with semicircles on each end. Find x and y exact and approximate values

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Question 901357: Dimensions that will produce a rectangular area of 100 Pi from a 300 meter track with semicircles on each end. Find x and y exact and approximate values
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The circumference of a circle plus two equal sides of a rectangle sum to 300 meters.

x = the diameter of each semicircle, and a capped side of the rectangle.
y = the uncapped side of the rectangle.

The radius of the equivalent circle is x/2; so the contribution to perimeter of each semicircle occurs TWICE, meaning the perimeter contribution is from a whole circle. This distance is 2%2Api%2A%28x%2F2%29=x%2Api.

The track perimeter includes the "circumference just discussed PLUS the uncapped rectangle lengths of y...

highlight_green%282y%2Bx%2Api=300%29.

ALSO given, highlight_green%28xy=100pi%29;

Two equations and two unknowns in x and y.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions that will produce a rectangular area of 100 Pi from a 300 meter track with semicircles on each end. Find x and y exact and approximate values


Exact dimensions to produce a rectangular area of 100pi: highlight_green%28highlight_green%28%28300%2B-sqrt%2890000+-+800pi%5E2%29%29%2F2pi%29%29

Approximate dimensions to produce a rectangular area of 100pi: highlight_green%28highlight_green%282.1425m_by_146.6346m%29%29   OR   highlight_green%28highlight_green%2893.35m_by_3.365m%29%29

You can do the check!! 



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