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Rudiy27
2 years ago
5

One of the legs of a right triangle has length 4 cm. Express the length of the altitude perpendicular to the hypotenuse as a fun

ction of the length of the hypotenuse
Mathematics
1 answer:
bezimeni [28]2 years ago
6 0

Without loss of generality, we can think of the 4 cm leg of the triangle as being the short leg. It is also the hypotenuse of the smallest of the similar triangles created by the altitude (x). If h represents the hypotenuse of the triangle, then similarity tells us the ratio of the "long" leg to the hypotenuse is the same for the smallest and largest triangles.

... x/4 = √(h²-4²)/h

Then the altitude (x) as a function of the hypotenuse (h) is ...

... x = (4/h)×√(h²-16)

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