How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10- foot tall wall?

Question

 How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10- foot tall wall?

Answer 1

Think of this problem like a right triangle. The house to the base of the ladder is one horizontal edge (X), the wall of the house is the other vertical edge (10), and these connect to form a right angle on the ground. And the length of the ladder is the hypotenuse (13).

Now, use Pythagorean theorem, where x^2 + 10^2 = 13^2

x^2 = 169 -100

x = +/- sqrt(69); however, we only keep the positive value as you cannot have a negative ladder!

How this helps!