A rectangle’s area is 1.8 times the area of a square whose side is 20 cm. The rectangle’s length is 5 times its breadth. Find the rectangle’s perimeter.

Introduction / Context:We are given a rectangle whose area relates directly to the area of a known square, along with a length–breadth ratio. That allows us to solve for the rectangle’s dimensions and then compute its perimeter straightforwardly.

Given Data / Assumptions:

• Square side = 20 cm ⇒ A_square = 20^2 = 400 cm^2.
• Rectangle area A_rect = 1.8 * 400 = 720 cm^2.
• Length L = 5B (B = breadth).

Concept / Approach:Substitute L = 5B into A_rect = L * B = 5B^2 to solve for B. Then compute L and finally the perimeter 2(L + B).

Step-by-Step Solution:5B^2 = 720 ⇒ B^2 = 144 ⇒ B = 12 cmL = 5 * 12 = 60 cmPerimeter P = 2(L + B) = 2(60 + 12) = 144 cm

Verification / Alternative check:Check area: 60 * 12 = 720 cm^2, which is 1.8 * 400 cm^2, as required.

Why Other Options Are Wrong:145, 133, and 135 cm do not correspond to any integer B satisfying 5B^2 = 720.

Common Pitfalls:Using 1.8 as 1.08 accidentally; or forgetting to double when computing 2(L + B).

Final Answer:144 cm