A 10-foot ladder is leaning up a wall. The distance the ladder is from the wall is 2 feet shorter than the distance the ladder reaches on the wall. What is the distance the ladder reaches up the wall?

Answer 1

h = distance up the wall

Note you have a right triangle with hypotenuse of 10, height h, and base h-2. Then

h² + (h - 2)² = 10² = 100

h² + (h² - 4h + 4) = 100

2h² - 4h - 96 = 0 ⇒

h² - 2h - 48 = 0

(h - 8)(h + 6) = 0

h = 8 ft