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

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)

Answer 1

Given:

The length of a certain rectangle is decreased by 4 cm and the breadth is increased by 2 cm,

It would result in a square of the same area

Concept used:

Area of rectangle = L × B

Area of square = Side × Side

Perimeter of rectangle = 2(L + B)

Calculations:

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.