Question

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 3cm and 27cm long. Find the length of the altitude to the hypotenuse.

Answer 1

To find the length of the altitude, we have to use the ratios of the similar sides.
Let the length of altitude=x
Ratio of sides:

`(x)/(3) = (27)/(x) \\ Cross \ multiply \\ x^(2) =81 \\ Take \ square \ root.\\ √(x^2)= √(81) \\ x=9 \\`
So length of altitude is 9 cm.

Answer: 9 cm