The sum of the legs of a right-angled triangle is 19 cm, and their difference is 3 cm. Find the area of this triangle.

Let one of the legs of a right-angled triangle be equal to X cm, and the other leg is equal to Y cm.

By condition, X + Y = 19 cm, X – Y = 3 cm.

Let’s solve the system of two equations by the addition method.

{X + Y = 19.

{X – Y = 3.

X + Y + X – Y = 19 + 3.

2 * X = 22.

X = 22/2 = 11 cm.

Y = 19 – 11 = 8 cm.

Determine the area of a right-angled triangle.

S = X * Y / 2 = 11 * 8/2 = 44 cm2.

Answer: The area of the triangle is 44 cm2.