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

Algebra ->  Surface-area -> 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      Log On


   

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) About Me  (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 x%5E2 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 pi%2Ar%5E2=pi%2A%28x%2F2%29%5E2 square yards.

So in total, the complete area of this oval is x%5E2%2Bpi%2A%28x%2F2%29%5E2

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

x%5E2%2Bpi%2A%28x%2F2%29%5E2+=+1300

solve that equation for x to get your answer.