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.

#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!