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:
$\frac{x}{3} = \frac{27}{x} \\ Cross \ multiply \\ x^{2} =81 \\ Take \ square \ root.\\ \sqrt{x^2}= \sqrt{81} \\ x=9$
So length of altitude is 9 cm.

Answer: 9 cm