In a right‑angled triangle, an altitude drawn to the hypotenuse divides it into segments of 9 cm and 16 cm. Find the lengths of the two legs of the triangle.

Step-by-step solution

1. Let the altitude be $h$, and the segments of the hypotenuse be $p=9$ cm and $q=16$ cm.
2. Use the property: $h^2=p\times q$. Compute $h^2=9\times 16=144$, so $h=12$ cm.
3. Leg adjacent to segment $p$ is $\sqrt{p(p+q)}=\sqrt{9\times 25}=\sqrt{225}=15$ cm.
4. Leg adjacent to segment $q$ is $\sqrt{q(p+q)}=\sqrt{16\times 25}=\sqrt{400}=20$ cm.
5. Hence the two legs are 15 cm and 20 cm.

Concept tested: Altitude to hypotenuse in right triangle

Published 10 October 2026 · How this solution was prepared and checked