If the length of certain rectangle is decreased by 4 cm and breadth is increased by 2 c, it would result in a square of the same area. What is the perimeter of the original rectangle?

Solution

Let length be L and breadth be B,  Since the sides of the square are equal,  ⇒ L − 4 = B + 2  ...........(1)  ⇒ L = B + 6  The area of the rectangle is equal to the area of the square,  L × B = (L - 4)(B + 2)  ⇒ (B + 6)(B) = (B + 6 - 4)(B + 2)   ⇒ B2 + 6B = (B + 2)2   ⇒ B2 + 6B = B2 + 4B + 4 ⇒ 6B = 4B + 4   ⇒ 2B = 4 ⇒ B = 2 cm then form (1) we get, ⇒ L - 4 = B + 2 ⇒ L - 4 = 2 + 2 ⇒ L = 4 + 4 = 8 cm Now the Perimeter of the rectangle, ⇒ P = 2(8 + 2) ⇒ P = 2(10) = 20 cm ∴ The perimeter of the original rectangle is 20 cm.