The bisector of a right-angled triangle, drawn from the vertex of the right angle, divides the hypotenuse

The bisector of a right-angled triangle, drawn from the vertex of the right angle, divides the hypotenuse of 13 cm in a ratio of 5/12. What is the area of a right triangle?

And so the angle C = 90 degrees.
CD bisector. CD: DB = 5: 12
AB = 13cm
Accept AC = 5x BC = 12x
According to the theory of Pythagoras, we get the following expression:
(5x) ^ 2 + (12x) ^ 2 = 25x ^ 2 + 144x ^ 2 = 169 then x will be equal to 1cm
then AC = 5x = 5cm BS = 12x = 12cm
The area is equal to (АСхBC) / 2 = (5Х12) / 2 = 30cm2