The area of a rectangular field is 460 sq m. The length of the rectangle is 15% more than its breadth. Find the breadth of the rectangle in metres, assuming length = 1.15 * breadth and area = length * breadth.

Introduction / Context:This question tests translating percentage relationships into algebra and solving for dimensions using area. If length is 15% more than breadth, then length = breadth + 15% of breadth = 1.15 * breadth. Substitute this into the area formula area = length * breadth to get a quadratic in breadth, then solve and choose the physically meaningful positive value.

Given Data / Assumptions:

• Area = 460 sq m
• Length is 15% more than breadth
• So length l = 1.15 * b
• Area formula: A = l * b

Concept / Approach:Replace l in A = l*b with 1.15b. Then solve 1.15b^2 = 460 for b. Keep units in metres throughout.

Step-by-Step Solution:

Verification / Alternative check:If breadth b = 20, then length l = 1.15 * 20 = 23 m. Area = 23 * 20 = 460 sq m, matching perfectly. Also, length is indeed 3 m more than breadth, which is 15% of 20.

Why Other Options Are Wrong:

Common Pitfalls:Common mistakes include interpreting “15% more” as “add 15 metres” instead of multiplying by 1.15, or using 0.15b instead of 1.15b for the length. Another error is mishandling 460/1.15; converting 1.15 into a fraction (115/100) makes division cleaner and avoids rounding errors.

Final Answer:20 m