The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?

### Concept & Algebra Express the relationship between the length and breadth algebraically, then substitute it into the area formula to solve for the missing dimension. $$ \text{Area} = l \times b $$ ### Step-by-Step Solution * Let the breadth of the rectangular field be $b$. * The length is 15% more than the breadth, meaning: $$ l = b + 0.15b = 1.15b $$ * We are given the area: $$ l \times b = 460 $$ * Substitute $l$: $$ (1.15b) \times b = 460 $$ $$ 1.15b^2 = 460 $$ * Solve for $b^2$: $$ b^2 = \frac{460}{1.15} = \frac{46000}{115} = 400 $$ * Solve for $b$: $$ b = \sqrt{400} = 20 \text{ metres} $$ * The breadth is $20$ metres. This value does not match options a, b, or c. ### Exam Strategy & Shortcut $15\%$ is $\frac{3}{20}$. So if breadth is $20x$, length is $23x$. Area = $20x \times 23x = 460x^2$. Setting this to $460$ gives $x^2 = 1 \implies x = 1$. The breadth is $20 \times 1 = 20$. This completely bypasses decimal division. ### Common Pitfall Incorrectly setting up the "15% more" condition as just $0.15b$ instead of $1.15b$. Alternatively, finding the value of 20 and hastily selecting "Cannot be determined" when they don't see it in the first few options, instead of "None of these". ### Final Answer Therefore, the correct answer is **None of these**.