# When the base of a ladder is 4 m from the wall, a window 16 m high can be reached. Where should the base be if a window 18 m high has to be reached.

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### 1 Answer

When the base of a ladder is 4 m from the wall a window 16 m high can be reached. The wall, the ground and the ladder form a right triangle where the ladder is the hypotenuse. If the length of the ladder is L, L^2 = 4^2 + 16^2 = 272

Let the distance from the wall where the base should be to allow the ladder to be used to reach a window 18 m high be x, using Pythagoras' Theorem:

x^2 + 18^2 = L^2 = 272

=> x^2 = 272 - 324

This gives a negative value for x showing that the ladder cannot be used to reach a window that is 18 m high. The maximum height that can be reached using the ladder is 16.49 m

**The ladder cannot be used to reach a window 18 m high.**