Hello all, thank you for your time and help. I have no idea how to find this, as, since the lengths of the two legs cannot be congruent, you have two variables (X and Y, one variable per leg).

The altitude of a right triangle divides the hypotenuse into two segments whose lengths are 9 cm and 16 cm. Find the lengths of the two legs.

Thank you all for your help!

2. If the two segments are 9 and 16, then the hypotenuse is 25. If it's a right triangle, then it is probably a 7-24-25 right triangle.

3. Originally Posted by pyrosilver
If the two segments are 9 and 16, then the hypotenuse is 25. If it's a right triangle, then it is probably a 7-24-25 right triangle.
Yes, if the two segments are 9 and 16 of course the hypotenuse is 25. Are you saying the legs are 7 and 24? Thank you, but how did you come to this conclusion?

4. I believe you are right since $\displaystyle 7^2 + 25^2=625$ which is $\displaystyle 25$ squared, but I'm not sure of the formula to find that. Thank you

5. sorry i meant $\displaystyle 7^2 + 24^2 = 25^2$

6. 7-24-25 is one of the "special right triangles" -- the most basic and the most known. (3-4-5, 7-24-25, i think 8-12-13) etc.