In a triangle ABC (LC = 90 degrees) AB = 10cm, the radius of the inscribed circle is 2cm. Find: S (area) of this triangle.

The radius of the inscribed circle in a right-angled triangle is: OH = (CB + AC – AB) / 2 = 2 cm.
Let us express from the formula the sum of AC + CB.
AC + CB = 2 * 2 + AB = 4 + 10 = 14 cm.
Let AC = X cm, then CB = 14 – X cm.
By the Pythagorean theorem, AB2 = AC2 + CB2.
100 = X2 + (14 – X) 2.
100 = X2 + 196 – 28 * X + X2.
2 * X2 – 28 * X + 96 = 0.
X2 – 14 * X + 48 = 0.
Let’s solve the quadratic equation.
X1 = 6 cm.
X2 = 8 cm.
Let AC = 8 cm, then CB = 6 cm.
Determine the area of the triangle.
Savs = AC * SV / 2 = 48/2 = 24 cm2.
Answer: The area of the triangle is 24 cm2.