The hypotenuse of a right-angled triangle is 15 cm, and one of the legs is 3 cm smaller than the other. find the legs.

1. Let’s denote the first leg of a right-angled triangle by x.

2. Determine the length of the second leg.

(x – 3) cm

3. Using the Pythagorean theorem, compose and solve the equation.

x ^ 2 + (x – 3) ^ 2 = 15 ^ 2;

x ^ 2 + x ^ 2 + 6x + 9 = 225;

2x ^ 2 + 6x + 9 – 225 = 0;

2x ^ 2 + 6x – 216 = 0;

D = 6 ^ 2 – 4 * 2 * (- 216) = 36 + 1728 = 1764;

x1 = (- 6 + 42) / (2 * 2) = 36/4 = 9;

x2 = (- 6 – 42) / (2 * 2) = – 48/4 = – 12 – does not satisfy the condition of the problem.

4. The first leg of a right-angled triangle is x = 9 cm.

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

9 – 3 = 6 cm.

Answer: the first leg of a right-angled triangle is 9 cm, the second leg is 6 cm.