Question

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet 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 15 feet.

Answer 1

The length of ladder is 17 feet .

Explanation:

Refer the attached figure .

Let the length of ladder AC be h

We are given that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder.

So ,Perpendicular = AB = h-9

Distance from the bottom of the ladder to the building= BC = Base =15 feet.

Using Pythagoras theorem

`Hypotenuse^2=Perpendicular^2+Base^2\\h^2=(h-9)^2+15^2\\h^2=h^2+81-18h+225\\18h=306\\h=(306)/(18)\\h=17`

Hence The length of ladder is 17 feet .