The area of a square is equal to the area of a rectangle. The rectangle’s length is 5 cm more than the side of the square, and the rectangle’s breadth is 3 cm less than the side of the square. Find the perimeter of the rectangle in cm, assuming both shapes have exactly the same area.

Introduction / Context:This problem combines algebra with mensuration. You are told a square and a rectangle have equal area, but the rectangle’s sides depend on the square’s side. The correct method is to let the square side be s, write the rectangle dimensions as (s + 5) and (s - 3), equate areas, solve for s, then compute the rectangle perimeter 2 * (l + b).

Given Data / Assumptions:

• Square side = s cm
• Rectangle length = s + 5 cm
• Rectangle breadth = s - 3 cm
• Areas are equal: s^2 = (s + 5)(s - 3)
• Perimeter of rectangle = 2 * (length + breadth)

Concept / Approach:Form an equation using equal areas, solve for s, then substitute to find rectangle sides and perimeter. Ensure the breadth stays positive (s must be greater than 3).

Step-by-Step Solution:

Verification / Alternative check:Square area = 7.5^2 = 56.25. Rectangle area = 12.5 * 4.5 = 56.25. Areas match, so the perimeter computed from these rectangle sides is consistent.

Why Other Options Are Wrong:

Common Pitfalls:Students often forget to expand correctly, or incorrectly cancel terms. Another mistake is using perimeter of square instead of rectangle. Also, do not assume s is an integer; s can be fractional as seen here.

Final Answer:34 cm