word problem help!

Question

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 16 feet.

Answer 1

Draw a picture and you will see that you have a right triangle and can use the Pythagorean Theorem.

Let x = the length of the ladder

Let x - 8 = the distance from the ground to the top of the ladder

a² + b² = c²

16² + (x - 8)² = x²

256 + x² - 16x + 64 = x²

-16x = -320

x = 20 feet