SOLUTION: The question is: An oval athletic field is the union of a square and semicircles at opposite ends, as shown in figure. If the total area of the field is 1,300 square yards, find t

Question 967609: The question is: An oval athletic field is the union of a square and semicircles at opposite ends, as shown in figure. If the total area of the field is 1,300 square yards, find the dimensions of the square. ( The figure does not have any dimensions) I know I am going to have to work "backwards", but I don't even know how to set this problem up.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Hint:

Let the square have a side length of x. Let x be some measurement in yards.

That means each semi-circle has a diameter of x, so each semi-circle has a radius of x/2

Here is what the drawing would look like

The area of the square is square yards.

If you take the two semi-circular ends and glue them together, you would form a full complete circle. The area of this circle is square yards.

So in total, the complete area of this oval is

"the total area of the field is 1,300 square yards" which tells us that

solve that equation for x to get your answer.
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