Area of a square is given as 12800 sq miles, find the time taken by a lady to…

Concept: For a square with side length a, the area is a2, and the diagonal is d = a√2 (from the Pythagorean theorem applied across the two adjacent sides). Time taken to cover a distance at a constant speed is time = distance ÷ speed.

1. Let the side of the square be a. Given area = a2 = 12800 sq miles.

2. So a = √12800 = √(6400 × 2) = 80√2 miles.

3. Diagonal d = a√2 = 80√2 × √2 = 80 × 2 = 160 miles.

4. Time = distance ÷ speed = 160 ÷ 15 = 32/3 ≈ 10.67 hours.

Cross-check: squaring the side back, (80√2)2 = 6400 × 2 = 12800 sq miles, matching the given area. Among the offered choices, 10 hours is nearest to the computed 10.67 hours (within about 6%), while 8, 8.5, and 9 hours are all farther off by 1.6 hours or more.

So the closest matching time is 10 hours.