In a right triangle, the altitude drawn to the hypotenuse divides it into segments of $9\text{ cm}$ and $16\text{ cm}$. Find the perimeter of the triangle.

Step-by-step solution

1. Use the property $h^2=xy$ where $x$ and $y$ are the two segments: $h^2=9\times 16=144$.
2. Find the altitude: $h=\sqrt{144}=12$ cm.
3. The hypotenuse is $x+y=9+16=25$ cm.
4. Find the legs using $a^2=xy$ formulas: $a^2=9\times 25=225⟹a=15$ cm and $b^2=16\times 25=400⟹b=20$ cm.
5. Add the three sides: $15+20+25=60$ cm.
6. Therefore the perimeter is $60$ cm.

Concept tested: Altitude to hypotenuse in a right triangle

Published 4 October 2026 · How this solution was prepared and checked