Find r of a circle inscribed in a right triangle with P = 24 cm and a hypotenuse of 10 cm.

From the condition it follows that the perimeter of this triangle is 24 cm, and the length of the hypotenuse is 10 cm, then the sum of the lengths of the first and second legs is:
24 – 10 = 14 cm.
It is known that the radius of the inscribed circle will be equal to:
r = (a + b – c) / 2, where a, b – legs, c – hypotenuse.
Find the length of the radius:
r = (14 – 10) / 2 = 2 cm.
Answer: the length of the radius of the inscribed circle is 2 cm.