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

Question

8699 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-26T21:42:56

This is a systems of equations problem.

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:

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)#. Find the hypotenuse of the triangle.

Good luck!