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

June 28, 2021 | education

| **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.

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