Area of a square natural lake is 50 sq. kms. A diver wishing to cross the lake diagonally, will have to swim a distance of

### Concept & Geometry This question tests the area-to-diagonal relationship of a square and tests unit conversion awareness (kilometers to miles). $$ \text{Area} = \frac{1}{2} d^2 $$ ### Step-by-Step Solution * **Step 1:** The area of the square lake is given as $50 \text{ km}^2$. * **Step 2:** Using the formula relating area and diagonal ($d$): $\frac{1}{2} d^2 = 50$. * **Step 3:** $d^2 = 100$, so the diagonal $d = 10 \text{ km}$. * **Step 4:** The options are given in miles. Convert kilometers to miles (approximate conversion factor: $1 \text{ mile} \approx 1.609 \text{ km}$). * **Step 5:** Distance in miles $= \frac{10}{1.609} \approx 6.21 \text{ miles}$. * **Step 6:** Since $6.21 \text{ miles}$ does not match any of the given numeric options ($10, 12, 15$), the correct choice is "None of these". ### Exam Strategy & Shortcut As soon as you calculate $d = 10 \text{ km}$, immediately check the units in the options. Realize that $10 \text{ km}$ is definitely less than $10 \text{ miles}$ (since a mile is longer than a kilometer). Therefore, options a, b, and c are impossible without any complex calculations. ### Common Pitfall The most common mistake is ignoring the unit change and carelessly selecting "10 miles" after calculating a value of $10$, forgetting that the calculation yielded kilometers. ### Final Answer Therefore, the correct answer is **None of these**.