# 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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.