Step 1:

Let  is the length of the ladder.

is the distance between the bottom of the ladder and wall is m.

 is the distance from the top of the ladder to ground.

ladder slides away from ground at a rate of change is m/s.

The ladder slides down vertical at a rate of change m/s.

From Pythagoras theorem,

Differentiate each side with respect to t.

Length of the ladder is constant.

Substitute , and in above equation.

m.

Step 2:

Substitute , values in .

m.

Solution:

Length of the ladder m.