Triangle Problem?

Question

A 25 foot ladder is leaned against a vertical wall of a building. The foot of the ladder is 7 feet from the base of the building. If the ladder slides along the floor so that the top of the ladder if 4 feet lower than it used to be, how many feet did the base of the ladder slip?

Answer 1

For the current situation, draw a right triangle ABC.

Let AB = h be the vertical wall of a building.

AC is the ladder and BC is the distance between the wall and the ladder.

From pythagoras theorem : AC² = AB² + BC².

25² = h² + 7²
h² = 625 - 49

h² = 576
h = 24.

The ladder slides along the floor so that the top of the ladder if 4 feet lower than , then h = 20.

Let BE = b.

Triangle BDE is a right angle triangle.

From pythagoras theorem : BD² = BE² + DE².

20² + b² = 25²
b² = 625 - 400

b² = 225

b = 15.

b = BE = BC + CE = 7 + CE        (From the diagram)

15 = 7 + CE

CE = 15 - 7 = 8.

So, the ladder slip is 8 '.