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: Find the side of the square lake.
The lake is square shaped with area \(50\) sq. km. If the side length is \(s\),
\[ s^2 = 50 \implies s = \sqrt{50} = 5\sqrt{2} \text{ km} \]

Step 2: Find the diagonal.
For a square, the diagonal equals the side times \(\sqrt{2}\):
\[ d = s\sqrt{2} = 5\sqrt{2} \times \sqrt{2} = 5 \times 2 = 10 \text{ km} \]

Step 3: Convert kilometres to miles.
The question gives the area in kilometres but the answer choices in miles, so the km figure has to be converted before comparing. Using \(1 \text{ mile} \approx 1.6 \text{ km}\):
\[ 10 \text{ km} = \frac{10}{1.6} \text{ miles} = 6.25 \text{ miles} \]

Step 4: Compare with the given options.
The options offered are 10, 12, and 15 miles, but the actual swimming distance works out to 6.25 miles, which matches none of them.

Final Answer:
The diver has to swim 6.25 miles, which is not listed among the first three options.
\[ \boxed{\text{None of these}} \]