Question

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

Answer 1

This is a systems of equations problem.

Explanation:

Assuming the length is x and the width is y.

`2x + 2y = 18`
`xy = 20`

`2y = 18 - 2x`

`y = 9 - x`

`x(9 - x) = 20`

`9x - x^2 = 20`

`0 = x^2 - 9x + 20`

`0 = (x - 5)(x - 4)`

`x = 5 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!