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

1 Answer
Feb 26, 2016

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!