SOLUTION: The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 6 and 9. What is the length of the altitude?

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Question 873353: The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 6 and 9. What is the length of the altitude?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That altitude splits the right triangle into two similar right triangles.
Their acute angles have the same measure as those of the original, larger triangle.
The two smaller, split triangles are similar to the original, larger triangle, and to each other.
Their leg lengths ratios are the same:
x%2F6=9%2Fx --> x%2Ax=9%2A6 --> x%5E2=54 --> x=sqrt%2854%29=3sqrt%286%29=about7.348 .
The altitude's length is highlight%28sqrt%2854%29=3sqrt%286%29=about7.348%29