Pythagorean Theorem: Finding Ladder Length with 9m Height and 12m Base Distance

Question

A ladder leans against a wall, meeting the wall at a height of 9 meters. The base of the ladder is 12 meters from the wall. How long is the ladder?

To find the length of the ladder (hypotenuse), use the Pythagorean theorem: $a^2 + b^2 = c^2$ .

Given: $a = 9$ meters, $b = 12$ meters.

Substitute the known values into the equation: $9^2 + 12^2 = c^2$ .

Calculate: $81 + 144 = c^2$ .

Simplify: $225 = c^2$ .

Find $c$ : $c = \sqrt{225}$ .

Therefore, the length of the ladder is $15$ meters.

15 meters