The perimeter of a right-angled triangle is 48 cm, the hypotenuse is 20 cm, find the area.

1. A, B, C – the vertices of the triangle. S – area. P is the perimeter.

2. We take the length of the leg AB for x, for y – the length of the leg AC.

Their total length is P – BC = 48 – 20 = 28 cm.

3. We compose two equations:

x + y = 28;

x² + y² = 400;

4. We square both sides of the first equation:

(x + y) ² = 28²;

x² + 2xy + y² = 784;

5. Subtract the second equation from the resulting equation:

x² + 2xy + y² – x² – y² = 384;

2xy = 384;

xy = 192.

6. S = xy / 2 = 192: 2 = 96 cm².

Answer: S = 96 cm².