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

1. Let one leg of a right-angled triangle be x centimeters, then the second leg will be (x + 7) centimeters.
2. Let’s use the Pythagorean theorem c ^ 2 = a ^ 2 + b ^ 2 (where c is the hypotenuse of a right triangle, a and b are legs):
13 ^ 2 = x ^ 2 + (x + 7) ^ 2;
169 = x ^ 2 + x ^ 2 + 14 * x + 49;
2 * x ^ 2 + 14 * x – 120 = 0;
D = 14 ^ 2 – 4 * 2 * (- 120) = 196 + 960 = 1156 = 34 ^ 2;
x1 = (- 14 + 34) / 2 * 2 = 20/4 = 5;
x2 = (- 14 – 34) / 2 * 2 = – 12 (does not make sense);
3. One leg is x = 5, then the second is:
x + 7 = 5 + 7 = 12;
4. Answer: the legs are 5 cm and 12 cm.