equation to find height

Question

A ladder is leaning against a building . The distance from the bottom of the ladder to the building is 8ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 4ft less than the length of the ladder

Answer 1

Using the Pythagorean Theorem:

 

h² = (h - 8)² + (h - 4)²

h² = h² - 16h + 64 + h² - 8h + 16

 

Combine like terms

Set equal to zero

Solve for h.