Ladder Problems

Question

1. A ladder is leaning against a building. The distance from the bottom of the stairs to the building is 32 feet less than the length of the stairs and the top of the stairs is 4 feet less than the length of the stairs. Determine the length of the ladder

Answer 1

I will get you started. This problems describes a right triangle with the following dimensions:

L = length of hypotenuse = length of ladder = ?

L - 32 = base

L - 4 = height

Now you know that

L² = (L - 4)² + (L - 32)²

Expand this, collect like terms, simplify, and you will end up with a quadratic equation in L, which you can solve using the quadratic formula. Can you finish from here?