Question

The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the segment, formed by the altitude to the hypotenuse that is adjacent to the other leg?

Answer 1

Answer:

  21 cm

Step-by-step explanation:

Call the triangle ABC, with the right angle at B, the hypotenuse AC=25, and the given leg AB=10. The altitude to the hypotenuse can be BD. Since the "other leg" is BC, we believe the question is asking for the length of DC.

The right triangles formed by the altitude are all similar to the original. That means ...

  AD/AB = AB/AC . . . . . . ratio of short side to hypotenuse is a constant

Multiplying by AB and substituting the given numbers, we get ...

  AD = AB²/AC = 10²/25

  AD = 4

Then the segment DC is ...

  DC = AC -AD = 25 -4

  DC = 21 . . . . . centimeters