Answer:
3.2 ft
Step-by-step explanation:
The initial distance from the base of the ladder to the wall is:
[tex]20^2=16^2+d^2\\d=12\ ft[/tex]
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:
[tex]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[/tex]
Therefore, the top of the ladder is 3.2 ft higher now.
