Question

How long must a ladder be if it is to be leaned against a house at a point 9 ft above the ground resting 3 ft from the bottom edge of the wall?

Answer 1

9.5 feet

Explanation:

We have that,

Height of the point at the wall where the ladder is leaned = 9 feet

Horizontal distance between the ladder and wall = 3 feet.

So, we get the right triangle as shown in the figure.

Using 'Pythagoras Theorem', i.e.
`hypotenuse^(2)=perpendicular^(2)+base^(2)`, we get,

`x^(2)=9^(2)+3^(2)`

i.e.
`x^(2)=81+9`

i.e.
`x^(2)=90`

i.e. x = 9.5 feet.

Thus, the length of the ladder must be 9.5 feet.