The hypotenuse of a right triangle is 15 cm and one of the legs is 3 cm smaller than the other. Find the legs of the triangle.

Let’s designate one of the legs as unknown x.

By the condition of the problem, the second leg is x – 3.

Next, we will use 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 ^ 2 + (x – 3) ^ 2 = 225

x ^ 2 + x ^ 2 – 6x + 9 = 225

2x ^ 2 – 6x – 216 = 0

Find the roots of the quadratic equation. 12 and -9. The leg value cannot be negative. Therefore, the required leg is 12. And the second is 9