One leg of a right-angled triangle is 2 cm larger than the other. Find the perimeter of this

One leg of a right-angled triangle is 2 cm larger than the other. Find the perimeter of this triangle if the hypotenuse is 10 cm.

Let’s designate one leg – x. Then the other can be expressed as x + 2. Let’s write down all the values based on the Pythagorean theorem:

x² + (x + 2) ² = 10²

Expand the brackets:

x² + x² + 4x + 4 = 100
x² + 2x – 48 = 0

We solve the resulting quadratic equation:

D = b² – 4ac = 4 + 192 = 196
x1 = (- 2 + 14) / 2 = 6;
x2 = (- 2 – 14) / 2 = – 8 – this root does not fit. The side of the triangle must be indicated by a positive number.

Leg: one 6 cm, the other 6 + 2 = 8 cm.Perimeter 6 + 8 + 10 = 24 cm