What would the length of the sides of a rectangle be if the perimeter and area are 72?

Question

I need to find the length of the sides of a rectangle if both the perimeter and area are 72

Answer 1

The area and perimeter of the rectangle is 72.

Area : A = l * b and Perimeter : P = 2(l + b), where l = length and b = breadth.

A = 72 and P = 72

l * b = 72 and 2(l + b) = 72

l = 72/b and (l + b) = 36.

(72/b) + b = 36

72 + b² = 36b

b² - 36b + 72 = 0

a = 1, b = - 36 and c = 72

x = [- b ± √(b² - 4ac)]/2a

b = [-(-36) ± √{(-36)² - 4(1)(72)}]/2(1)

b = [36 ± √(1008)]/2

b = (36 + 31.75)/2 and b = (36 - 31.75)/2

b = 33.875 and b = 2.125

If b = 33.875 then l = 72/b = 72/33.875 = 2.125 units.

If b = 2.125 then l = 72/b = 72/2.125 = 33.875 units.

The measurements of the rectangle are 2.175 units and 33.875 units.