Altitude to the hypotenuse
The question
h =
Find the length of the altitude h.
The altitude as a geometric mean
How it works.
big~left~right
same shape→same ratios
h² = p × q=18 × 32
√576=24
- 01
Dropping the altitude from the right angle onto the hypotenuse makes two smaller triangles. Each has a right angle, and each shares one of the original's acute angles — so all three triangles are similar.
- 02
Similar triangles have matching sides in the same ratio, so write the ratio for the pair you need.
- 03
For the altitude the ratio pairs it with the two pieces: h/p = q/h, so h² = p × q.
- 04
576 under the root gives 24.