Question

Area of a square natural lake is $50$ (square miles). 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 the above

Hint:

For a square, \(\text{diagonal} = \sqrt{2} \times \text{side}\). If area is known, side \(= \sqrt{\text{area}}\).

Answer 1

The Correct Option is A

Step 1: Find the side of the square from its area.
If the area is $50$, then side $s=\sqrt{50}$ miles.
Step 2: Use the diagonal formula for a square.
Diagonal $d = s\sqrt{2} = \sqrt{50} \sqrt{2}=\sqrt{100}=10$ miles. \[ \boxed{10\ \text{miles}} \]