The hypotenuse of a right-angled triangle is 13 cm. One of the legs is 7 more. Find the legs?

Let one of the legs be equal to x cm, then the other is equal to (x + 7) cm.

By the Pythagorean theorem, the square of the hypotenuse is:

13 ^ 2 = x ^ 2 + (x + 7) ^ 2.

Find x.

x ^ 2 + x ^ 2 + 14 * x + 49 – 169 = 0.

2 * x ^ 2 + 14 * x – 120 = 0.

x ^ 2 + 7 * x – 60 = 0.

x1,2 = (- 7 ± √ (49 – 4 * (- 60))) / 2 = (- 7 ± 17) / 2.

x1 = (- 7 + 17) / 2 = 5.

x2 = (- 7 – 17) / 2 = – 12. – does not fit, since the side cannot have a negative value.

Thus, the first leg is 5 cm, the second leg is 5 + 7 = 12 cm.

Verification:

13 ^ 2 = 5 ^ 2 + 12 ^ 2.

169 = 169.