# The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width?

Feb 26, 2016

This is a systems of equations problem.

#### Explanation:

Assuming the length is x and the width is y.

$2 x + 2 y = 18$
$x y = 20$

$2 y = 18 - 2 x$

$y = 9 - x$

$x \left(9 - x\right) = 20$

$9 x - {x}^{2} = 20$

$0 = {x}^{2} - 9 x + 20$

$0 = \left(x - 5\right) \left(x - 4\right)$

$x = 5 \mathmr{and} 4$

The width can either be 4 or 5 feet.

Practice exercises:

1. The area of a rectangle is 108 square feet and the perimeter is 62 feet. Find the distance between the two corners (the distance of the diagonals).

2. A right triangle has an area of 22 feet and a perimeter of $15 + \sqrt{137}$. Find the hypotenuse of the triangle.

Good luck!