The hypotenuse of a right-angled triangle is 13cm, one of the legs is 7cm larger than the other.

The hypotenuse of a right-angled triangle is 13cm, one of the legs is 7cm larger than the other. Find the legs of a right-angled triangle.

1. Length of the hypotenuse of a right-angled triangle: C = 13 cm;

2. The length of the first leg is equal to: K1 cm;

3. Length of the second leg: K2 = (K1 + 7) cm;

4. We apply the Pythagorean theorem:

K1² + K2² = C²;

K1² + (K1 + 7) ² = 13²;

K1² + (K1² + 2 * K1 * 7 + 7²) = 169;

2 * K1² + 14 * K1 + 49 – 169 = 0;

K1² + 7 * K1 – 60 = 0;

K11.2 = -3.5 + – √ ((- 3.5) ² + 60) = -3.5 + – 8.5;

There are no negative legs in a triangle;

K1 = -3.5 + 8.5 = 5 cm;

K2 = K1 + 7 = 12 cm.

Answer: the legs in a right-angled triangle are 5 cm and 12 cm.