# The perimeter of a rectangle is 30 inches and its area is 54 square inches. How do you find the length of the longest side of the rectangle?

Apr 8, 2016

9 inches

#### Explanation:

Let's begin by considering the perimeter (P) of the rectangle.

Let the length be l and the breadth be b.

Then P = 2l + 2b = 30

we can take out a common factor of 2 : 2(l+b) = 30

dividing both sides by 2 : l + b = 15 → b = 15 - l

now consider the area (A) of the rectangle.

$A = l \times b = l \left(15 - l\right) = 15 l - {l}^{2}$

The reason for writing b = 15 - l , was so that we would have an equation involving only one variable.

Now have to solve : $15 l - {l}^{2} = 54$

multiply by -1 and equate to zero.

hence ${l}^{2} - 15 l + 54 = 0$

To factor require 2 numbers that multiply to 54 and sum to -15.

rArr (l - 6)(l - 9 ) = 0 → l= 6 or l = 9

hence length = 9inches and breadth = 15-9 = 6inches.