Find the legs of a right-angled triangle if their sum is 46 cm, and the hypotenuse of the triangle is 34 cm.

In order to find the legs of a right-angled triangle, if it is known that their sum is 46 cm, and the hypotenuse of the triangle is 34 cm, we will apply the Pythagorean theorem.

The Pythagorean theorem says that the square of the hypotenuse is equal to the sum of the squares of the legs.

Let’s denote one of the legs as x cm, then (46 – x) cm the second leg.

We get the equation:

x ^ 2 + (46 – x) ^ 2 = 34 ^ 2;

x ^ 2 + 2116 – 92x + x ^ 2 = 1156;

x ^ 2 + x ^ 2 – 92x + 2116 – 1156 = 0;

2x ^ 2 – 92x + 960 = 0;

x ^ 2 – 46x + 480 = 0;

D = 2116 – 1920 = 196;

x1 = (46 – 14) / 2 = 32/2 = 16;

x2 = (46 + 14) / 2 = 60/2 = 30.

16 and 30 cm legs.