Question

A ladder rests against a vertical wall at a height of 12 meters from the ground with its foot at a distance of 9 meters from the wall on the ground. If the foot of the ladder is shifted 3 mters awy from the wall, how much lower will the ladder slide down

Answer 1

This is similar to a right angle triangle, with the length of the ladder being the hypotenuse and the point at which the top end rests on the wall being one side and the point at which it touches the ground from the wall being the other side.

We can find the length of the ladder using Pythagoras theorem.

Length of the ladder = sqrt (12^2 + 9^2) = sqrt (144 + 81) = sqrt 225 = 15.

Therefore, if the ladder slips by 3 m, then the base becomes 12m. As the length of the ladder does not change, the ladder drops by the same amount, because of the above, Pythagoras Theorem, since 9^2 + 12^2 = 15^2.

Thus, the ladder slides down by 3m on the wall.

Answer 2

Using Pythagoras theorem,
Ladder's length ^ 2= height ^ 2 + foot distance ^ 2
=12^2+9^2
=144 + 81
=225
Therefore length of ladder is root 225
=15m
If the foot distance is increased by 3m then the total foot distance is 9+3=12m
Therefore again using Pythagoras theorem
Height ^2 = ladder ^2 - foot ^2
=15^2 - 12^2
=225-144
=81
Therefore, height is root of 81 which is 9m.
Therefore, the ladder will slide down by
12-9
=3m.

Hope it helps..... :)