The leg of a right-angled triangle is 10 cm larger for the second leg and 10 cm smaller

The leg of a right-angled triangle is 10 cm larger for the second leg and 10 cm smaller from the hypotenuse. Find the sides of this triangle.

Let the first leg be x, then the second leg is x-10, and the hypotenuse is x + 10. Knowing that the sum of the squares of the legs is equal to the square of the hypotenuse, we can compose the equation:
x ^ 2 + (x-10) ^ 2 = (x + 10) ^ 2;
x ^ 2 + x ^ 2-20x + 100 = x ^ 2 + 20x + 100;
x ^ 2 + x ^ 2-20x + 100-x ^ 2-20x-100 = 0;
x ^ 2-40x = 0;
x * (x-40) = 0;
x1 = 0 – is not a solution, because leg length must be greater than 0.
x2 = 40.
Therefore, one of the legs of this right-angled triangle is 40 cm, the second is 40-10 = 30 cm, the hypotenuse is 40 + 10 = 50 cm.