Question

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:

• A. 10 miles
• B. 12 miles
• C. 15 miles
• D. None of these

Hint:

Find the diagonal in km first (side times \(\sqrt{2}\)), then convert to miles before comparing with the options.

Answer 1

The Correct Option is D

Step 1: Convert the area itself to square miles first.
Rather than convert the final distance, convert the area up front. Since $1 \text{ km} \approx 0.625$ miles (the reciprocal of $1.6$), one square kilometre is about $0.625^2 \approx 0.39$ square miles. So $50$ sq. km is about:
$$ 50 \times 0.39 \approx 19.5 \text{ sq. miles} $$

Step 2: Find the side length in miles.
$$ s = \sqrt{19.5} \approx 4.42 \text{ miles} $$

Step 3: Find the diagonal in miles.
$$ d = s\sqrt{2} \approx 4.42 \times 1.414 \approx 6.25 \text{ miles} $$

Step 4: Compare with the answer choices.
Both routes, converting the distance at the end or converting the area at the start, land on the same figure, about $6.25$ miles. None of the fixed options (10, 12, 15 miles) match this.

Step 5: Conclusion.
The diver actually swims close to $6.25$ miles, so the correct choice is none of these, not any of the three specific mile values offered.
$$ \boxed{\text{None of these}} $$