Rectangle with sides in the ratio 3:1 and perimeter 96 m: The length and breadth of a rectangle are in the ratio 3 : 1. If its total perimeter is 96 m, compute the exact length (in metres) of the rectangle.

Introduction / Context:This is a standard perimeter-to-dimensions problem for rectangles using a given side ratio. We translate perimeter information into algebraic equations and then identify the rectangle’s length.

Given Data / Assumptions:

• Length : Breadth = 3 : 1 → Let length = 3k and breadth = 1k.
• Perimeter P = 96 m.
• Perimeter formula: P = 2 * (L + B).

Concept / Approach:Substitute the ratio-based expressions into the perimeter formula to solve for k, then compute the length 3k.

Step-by-Step Solution:

Verification / Alternative check:With L = 36 m and B = 12 m, P = 2(36 + 12) = 2 * 48 = 96 m, which matches the given perimeter.

Why Other Options Are Wrong:24m and 12m are the breadth or its multiples; 48m and 40m do not satisfy the ratio and perimeter simultaneously.

Common Pitfalls:Forgetting to double the sum in the perimeter formula or mixing up length and breadth magnitudes (3k vs k).

Final Answer:36m