SOLUTION: Consider a rectangle that has a diagonal of 20 feet and a perimeter of 52 feet. Find the area of this rectangle.

Question 657795: Consider a rectangle that has a diagonal of 20 feet and a perimeter of 52 feet. Find the area of this rectangle.
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
let l be the length of the rectangle and w be the width of the rectangle. With the diagonal being 20 feet long, using the Pythagorean Theormem, we get

With a perimeter of 52 feet, we have

Substituting, we get

We can solve for w using the quadratic equation with a=2, b=-52, and c=276:

and , or
and
Both of these are basically the same solution with the l and w values being switched. So the area is:

The area is 138 square feet.

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