Question

a ladder is leaning against a building so that the distance from the ground to the top of the ladder is 1 ft 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 3 ft

Answer 1

Let x ft be the length of the ladder, then the distance from the ground to the top of it will be x-1 ft.

If the distance from the bottom of the ladder to the building is 3 ft, then we can apply Pythagoras:

x² = (x-1)² + 3² . Expand:
x² = x² - 2x + 1 + 9
x² = x² - 2x + 10

x² - x² =  - 2x + 10
0 = - 2x + 10
2x = 10  and x = 5 ft