The area of a rectangular triangle is 12 cm, and one of the legs is 2 cm larger than the other.

The area of a rectangular triangle is 12 cm, and one of the legs is 2 cm larger than the other. Find the length of the smaller leg.

1. Let’s denote the length of the smaller leg through x cm.

2. Determine the length of the larger leg:

(x + 2) cm.

3. Let’s compose and solve the equation:

((x + 2) * x) / 2 = 12;

(x + 2) * x = 12 * 2;

x ^ 2 + 2x = 24;

x ^ 2 + 2x – 24 = 0;

D = 2 ^ 2 – 4 * 1 * (-24) = 4 + 96 = 100

x1 = (-2 + √100) / (2 * 1) = (-2 + 10) / 2 = 8/2 = 4;

x2 = (-2 – √100) / (2 * 1) = (-2 – 10) / 2 = -12/2 = -6.

-6 – does not meet the condition of the problem.

4. The length of the smaller leg is 3.

Answer: the length of the smaller leg of a right-angled triangle is 6.