The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the leng

Question

Julli [10]

3 years ago

15

The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the leng

th of the shorter leg.

Mathematics

1 answer:

fomenos · Answer 1 · 2022-04-17T16:45:05+03:00

fomenos3 years ago

3 0

The altitude will be the geometric mean of the lengths, so
$h=\sqrt{4 \cdot 12}=4\sqrt{3}$ . The smaller leg is the hypotenuse of a right triangle sides 4 and $4 \sqrt{3},$ so the usual trig cliche, hypotenuse 8.

Answer: 8