What is maximum height on a wall a ladder that is 12 ft can reach if the foot of the ladder is 4 ft from the base of the wall.

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A ladder 12 ft in length is placed against a wall such that its base is 4 ft from the lowest point of the wall. The wall, the ladder and the ground form a right triangle. If the maximum height that the ladder can reach is H, the sides of the triangle are 4, H and 12 where 12 is the hypotenuse.

Using the Pythagorean Theorem,

4^2 + H^2 = 12^2

=> 16 + H^2 = 144

=> H^2 = 128

=> H = `8*sqrt 2`

=> H `~~` 11.31

**The maximum height that the ladder can reach is approximately 11.31 ft**

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