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

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) (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 .

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

.

ALSO given, ;

Two equations and two unknowns in x and y.
Answer by MathTherapy(10555) (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 :
Approximate dimensions to produce a rectangular area of : OR
You can do the check!!
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