One of the legs of a right-angled triangle is 12 cm and the hypotenuse is 6 cm larger than the other leg. Find the hypotenuse.

Let’s draw a triangle ABC, C – a right angle. AB – hypotenuse.
AC – 12 cm, let CB X cm, and AB (X + 6) cm.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.
Let’s make the equation
(X + 6) ^ 2 = X ^ 2 + 12 ^ 2
x ^ 2 + 12 x + 36 = x ^ 2 + 144
x ^ 2 + 12x – x ^ 2 = 144 – 36
12 x = 108
x = 108: 12 = 9
The leg is 9 cm.
Find the hypotenuse
9 + 6 = 15 cm
Answer: hypotenuse = 15 cm