The hypotenuse of a right-angled triangle is 12 cm. One of the legs of the triangle is 2 cm smaller than the other.

The hypotenuse of a right-angled triangle is 12 cm. One of the legs of the triangle is 2 cm smaller than the other. the perimeter of the triangle is 26cm. find the length of each leg.

Let one leg be x cm, then the second – (x – 2) cm.

The perimeter of a triangle is the sum of all its sides.

And we know the perimeter. the hypotenuse is also known.

x + (x – 2) + 12 = 26.

2x – 2 = 26 – 12.

2x = 14 + 2.

x = 8 cm – the length of the first leg.

The length of the second leg is 8 – 2 = 6 cm.

Let’s check the correctness of the calculations.

8 + 6 + 12 = 26 cm.

Answer: one leg is 8 cm, the second is 6 cm.