Questions: A rectangular pool at Andy's gym measures 25 meters by 50 meters. How many meters would Andy need to swim in order to swim diagonally across the pool?

Solution Steps

The dimensions of the rectangular pool are given as 25 meters by 50 meters. If Andy swims diagonally across the pool, the length and width of the pool form the legs of a right triangle, and the diagonal forms the hypotenuse. Thus, the two legs of the right triangle have lengths 25 meters and 50 meters.

Let the length of the diagonal be represented by \(d\). According to the Pythagorean theorem, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width). Therefore, \(d^2 = 25^2 + 50^2\)

\(d^2 = 625 + 2500\) \(d^2 = 3125\) \(d = \sqrt{3125}\) \(d = \sqrt{625 \times 5}\) \(d = 25\sqrt{5}\) \(d \approx 56.18\)

Final Answer