Question

The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 77 and 7. what is the length of the altitude?

Answer 1

`h=7√(11)\ units`

Explanation:

The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.

1st segment = 77 units

2nd segment = 7 units

Altitude = h units

So,

`h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=√(7\cdot 11\cdot 7)=7√(11)`