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?
1 Answer
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 = 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.
hence
#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.
