A rectangular swimming pool is 15 feet wide and has an unknown length. There is a 50 foot long drainpipe that crosses the pool diagonally under the floor of the pool. The pool and the pipe are shown in the image. What is the approximate length, "l", of the pool?
To find the length of the pool, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the width of the pool is 15 feet and the length we want to find is "l". The drainpipe acts as the hypotenuse. So, we have:
(15)^2 + l^2 = (50)^2
225 + l^2 = 2500
l^2 = 2275
l ≈ √2275
l ≈ 47.7 feet
Therefore, the approximate length of the pool is 47.7 feet.