One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 6 cm larger

One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 6 cm larger than the second leg, find the length of the hypotenuse.

From the condition it is known that one of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 6 cm larger than the second leg. In order to find the hypotenuse of a triangle, we compose and solve the equation using the Pythagorean theorem.

She says that the square of the hypotenuse is equal to the sum of the squares of the legs:

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

Let’s denote by x cm the length of the second leg and by (x + 6) cm the length of the hypotenuse.

We get the equation:

(x + 6) ^ 2 = x ^ 2 + 12 ^ 2;

x ^ 2 + 12x + 36 = x ^ 2 + 144;

x ^ 2 – x ^ 2 + 12x = 144 – 36;

12x = 108;

x = 108: 12;

x = 9 cm length of the second leg and (9 + 6) = 15 cm hypotenuse.