The perimeter of a rectangle is 41 inches and its area is 91 square inches. How do you find the length of its shortest side?

1 Answer
George C.
Jul 18, 2015

Use the conditions expressed in the question to form a quadratic equation and solve to find the lengths of the shortest (#13/2# inches) and longest (#14# inches) sides.

Explanation:

Suppose the length of one side is #t#.

Since the perimeter is #41#, the other side length is #(41 - 2t)/2#

The area is:

#t * (41-2t)/2 = 91#

Multiply both sides by #2# to get:

#182 = 41t - 2t^2#

Subtract the right hand side from the left to get:

#2t^2-41t+182 = 0#

Use the quadratic formula to find:

#t = (41+-sqrt(41^2 - (4xx2xx182)))/(2*2)#

#= (41+-sqrt(1681 - 1456))/4#

#= (41+-sqrt(225))/4#

#= (41+-15)/4#

That is #t = 26/4 = 13/2# or #t = 56/4 = 14#

So the shortest side is length #13/2# inches and the longest is #14# inches

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