Ladder

Geometry Level 2

A 12 feet long ladder is leaning against a wall so that its base is 4 feet from the wall at ground level (see figure above). How far up the wall does the ladder reach?

Note: Give your answer in feet.

129 \sqrt{129} None of these choices 8 2 8\sqrt{2} 160 \sqrt{160}

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A Former Brilliant Member by A Former Brilliant Member

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2 solutions

by the Pythagorean Theorem, we have

h 2 + 4 2 = 1 2 2 h^2 + 4^2 = 12^2

h 2 + 16 = 144 h^2 + 16 = 144

h 2 = 144 − 16 h^2 = 144 - 16

h 2 = 128 h^2 = 128

h = 128 = s q r t ( 64 ) ( 2 ) = 8 2 h = \sqrt{128} = sqrt{(64)(2)} = 8\sqrt{2} feet

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Relevant wiki: Pythagorean Theorem

Using the pythagorean theorem , we have

h = 1 2 2 − 4 2 = 128 = 64 ⋅ 2 = 8 2 ⋅ 2 = 8 2 h=\sqrt{12^2-4^2}=\sqrt{128}=\sqrt{64 \cdot 2}=\sqrt{8^2 \cdot 2 }=\boxed{8\sqrt{2}}

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