High School

The ratio of the segments into which the altitude to the hypotenuse of a right triangle divides the hypotenuse is 9:4. What is the length of the altitude?

A. 6
B. 36
C. 3
D. Cannot be determined

Answer :

The altitude to the hypotenuse divides the right triangle into two similar right triangles. The altitude is the geometric mean of the segment lengths of the hypotenuse. Here, we can say that the ratio of the altitude to those segments is
√(4*9) : 4 : 9 = 6 : 4 : 9
Since these are ratios, not measures, the actual length of the altitude cannot be determined. (4th selection)

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