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12-07-2018
Mathematics

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The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the length of the shorter leg.

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12-07-2018

The altitude will be the geometric mean of the lengths, so
[tex]h=\sqrt{4 \cdot 12}=4\sqrt{3}[/tex]. The smaller leg is the hypotenuse of a right triangle sides 4 and [tex]4 \sqrt{3},[/tex] so the usual trig cliche, hypotenuse 8.

Answer: 8

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