Jack swam directly across the pool diagonally from one corner to another. Which is the best estimate of how far he swam?

• A. 30 feet
• B. 50 feet
• C. 20 feet
• D. 40 feet

Answer: (B)

Think of the pool as a rectangle. The diagonal across the pool is the hypotenuse of a right triangle whose legs are the pool’s length and width. The distance across is found with the Pythagorean idea: diagonal ≈ sqrt(length^2 + width^2).

If the pool is about 40 ft long and 30 ft wide, you get sqrt(40^2 + 30^2) = sqrt(1600 + 900) = sqrt(2500) = 50 ft. So the best estimate is about 50 feet. This also fits a quick check: a 30-40-50 right triangle shows up when the sides are 30 and 40, giving a diagonal of 50. Since the diagonal is longer than either side, 50 ft makes sense as the distance across.