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

Answer:

The length of hypotenuse is $10\sqrt{6}$ cm

Step-by-step 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

$=\frac{3}{5}x$

Second part of hypotenuse length is

$=\frac{2}{5}x$

now, we can draw triangle

We can see that

triangles ABD and ABC are similar

so, the ratio of their sides must be equal

$\frac{\frac{3x}{5} }{12}=\frac{12}{\frac{2x}{5}}$

now, we can solve for x

$\frac{3x}{5}\times\frac{2x}{5}=144$

$6x^2=3600$

$x=10\sqrt{6}$

So,  

The length of hypotenuse is $10\sqrt{6}$ cm