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?
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 = lxxb = l (15 - l) = 15l - 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 :
# 15l - l^2 = 54#
multiply by -1 and equate to zero.
#l^2 - 15l + 54 = 0 #
To factor require 2 numbers that multiply to 54 and sum to -15.
hence length = 9inches and breadth = 15-9 = 6inches.