Question

A 20-foot ladder leans against a wall so that it is 16 feet high at the top. The ladder is moved so that the base of the ladder travels toward the

wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now? (Hint Let 12 – 2x be the distance from

the base of the ladder to the wall.)

х

2x

The top of the ladder is

feet higher now.

Answer 1

3.2ft higher

Explanation:

Answer 2

3.2 ft

Explanation:

The initial distance from the base of the ladder to the wall is:

`20^2=16^2+d^2\\d=12\ ft`

After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:

`20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft`

Therefore, the top of the ladder is 3.2 ft higher now.