One of the legs of a right-angled triangle is 21 cm, and the second leg is 7 cm less than the hypotenuse.

One of the legs of a right-angled triangle is 21 cm, and the second leg is 7 cm less than the hypotenuse. Find the perimeter of the triangle.

Suppose that the hypotenuse of this triangle is x cm, then the second leg will be equal to x – 7 cm.

Let’s use the Pythagorean theorem and compose the following equation:

21² + (x – 7) ² = x²,

441 + x² – 14 * x + 49 = x²,

490 – 14 * x = 0,

x = 490: 14,

x = 35 (cm) – the length of the hypotenuse of this triangle.

35 – 7 = 28 (cm) – the length of the second leg.

Thus, the perimeter of this triangle is:

P = 28 + 21 + 35 = 84 (cm).

Answer: 84 cm.