The perimeter of a right-angled triangle is 48 cm, and its hypotenuse is 20 cm. Find the legs.

From the condition it is known that the perimeter of a right-angled triangle is 48 cm, and it is also known that its hypotenuse is 20 cm. We need to find the legs of the triangle.

We start with what we denote by x the length of one of the legs, then the length of the second can be written as 48 – 20 – x = 28 – x cm.

Let’s apply the Pythagorean theorem to solve:

c ^ 2 = a ^ 2 + b ^ 2;

20 ^ 2 = x ^ 2 + (28 – x) ^ 2;

400 = x ^ 2 + 784 – 56x + x ^ 2;

2x ^ 2 – 56x + 384 = 0;

x ^ 2 – 28x + 192 = 0;

D = 784 – 768 = 16;

x1 = (28 + 4) / 2 = 16;

x2 = (28 – 4) / 2 = 24/2 = 12.

The legs are 16 cm and 12 cm.