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

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Answer 1 · 2016-02-26T21:42:56

This is a systems of equations problem.

Assuming the length is x and the width is y.

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

$2 y = 18 - 2 x$ $2y = 18 - 2x$

$y = 9 - x$ $y = 9 - x$

$x (9 - x) = 20$ $x(9 - x) = 20$

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

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

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

$x = 5 and 4$ $x = 5 and 4$

The width can either be 4 or 5 feet.

Practice exercises:

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

Good luck!