Geometry question

Question

for maximum safety the distance between the base of a ladder and building should be one-third of the length of the ladder. if a window is 20 feet above the ground how long a ladder is needed to meet the safety condition

Answer 1

Draw a right triangle with horizontal leg of length (1/3)x, vertical leg of length 20 and hypotenuse of length x.

Using the Pythagorean Theorem, we have:

[(1/3)x]² + 20² = x²

(1/9)x² + 400 = x²

(8/9)x² = 400

x² = 3600 / 8 = 450

x = √450 = √9√50 = 3√25√2 = 15√2 ft