Answer:
The length of hypotenuse is [tex]10\sqrt{6}[/tex] 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
[tex]=\frac{3}{5}x[/tex]
Second part of hypotenuse length is
[tex]=\frac{2}{5}x[/tex]
now, we can draw triangle
We can see that
triangles ABD and ABC are similar
so, the ratio of their sides must be equal
[tex]\frac{\frac{3x}{5} }{12}=\frac{12}{\frac{2x}{5}}[/tex]
now, we can solve for x
[tex]\frac{3x}{5}\times\frac{2x}{5}=144[/tex]
[tex]6x^2=3600[/tex]
[tex]x=10\sqrt{6}[/tex]
So,
The length of hypotenuse is [tex]10\sqrt{6}[/tex] cm
