Question

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 16 and 25. What is the length of the altitude?

Answer 1

Ahh got it!

Answer 2

BD/AD = AB/AC
CD/AD = AC/AB (inverse of above)

so BD/AD = AD/CD

Answer 3

BD*CD=AD^2
Now can you do it?

Answer 4

@Sunshine447

Answer 5

@apple_pi
I would do it in this way

a^2+b^2 = (16+25)^2
a^2 = c^2 + 16^2 -(1)
b^2 = c^2 + 25^2 -(2)
(1) + (2)
a^2 + b^2 = c^2 + 16^2 + c^2 + 25^2
(16+25)^2 = 2c^2 + 16^2 + 25^2