Question

If a 12 cm altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with ratio 3:2, what is the length of the hypotenuse

Answer 1

The length of hypotenuse is
`10√(6)` cm

Explanation:

Let's length of hypotenuse is x

Since, a 12 cm altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with ratio 3:2

so,

First part of hypotenuse length is

`=(3)/(5)x`

Second part of hypotenuse length is

`=(2)/(5)x`

now, we can draw triangle

We can see that

triangles ABD and ABC are similar

so, the ratio of their sides must be equal

`((3x)/(5) )/(12)=(12)/((2x)/(5))`

now, we can solve for x

`(3x)/(5)*(2x)/(5)=144`

`6x^2=3600`

`x=10√(6)`

So,

The length of hypotenuse is
`10√(6)` cm