The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Solution:
Let the length and breadth be x and y respectively

So, 2(x + y) : y = 5 : 1
⇒ (2x + 2y)/y = 5/1
⇒ 2x + 2y = 5y
⇒ 3y = 2x
⇒ y = 2x/3

Then,
Area = 216
⇒ x × y = 216
⇒ x × (2x/3) = 216
⇒ 2x² = 648
⇒ x² = 324
∴ x = 18