One of the legs of a right-angled triangle is 10 cm larger than the other and its area is 408 cm².

1. Let’s designate the smaller leg of a right-angled triangle through x cm.

2. Let’s define a larger leg:

(x + 10) cm.

3. Let’s compose and solve the equation:

(x * (x + 10)) / 2 = 408;

x ^ 2 + 10x = 408 * 2;

x ^ 2 + 10x = 816;

x ^ 2 + 10x – 816 = 0;

D = 100 + 4 * 816 = 100 + 3264 = 3364;

x1 = (-10 + 58) / 2 = 48/2 = 24;

x2 = (-10 – 58) / 2 = -68 / 2 = -32 – does not satisfy the condition of the problem.

4. The smallest leg of a right-angled triangle is 24 cm.

5. What is the largest leg of a right-angled triangle?

24 + 10 = 34 (cm).

Answer: the legs of a right-angled triangle are 24 cm and 34 cm.