Find the legs of a right-angled triangle if their sum is 35 and the hypotenuse is 25.

The condition says that we are given a right-angled triangular triangle. It is known that its hypotenuse is 25, and the sum of the legs is 35. And we need to find the length of the legs of the triangle.
To do this, we will apply the Pythagorean theorem, but first of all we will denote by x the degree measure of one of the legs, then we will write the length of the second as (35 – x).
Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
Substitute the values in the formula and solve the resulting equation:
x ^ 2 + (35 – x) ^ 2 = 25 ^ 2;
x ^ 2 + x ^ 2 – 70x + 1225 = 625;
2x ^ 2 – 70x + 600 = 0;
x ^ 2 – 35x + 300 = 0;
D = 1225 – 1200 = 25;
x1 = (35 + 5) / 2 = 20;
x2 = (35 – 5) / 2 = 15.
Answer: 15 and 20.