SOLUTION: the altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8 inches and 18 inches. how long is the altitude??? thank yo

Question 149657: the altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8 inches and 18 inches. how long is the altitude???
thank you !
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the two smaller triangles created by the altitude are similar to the original triangle (and each other)

using the similarity ratios, the altitude is the geometric mean of the two segments

8/a=a/18 __ "cross" multiplying __ a^2=144 __ taking square root __ a=12
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