The hypotenuse of a right-angled triangle is 20, find its leg if it is known that one of them is 4 larger than the other.

Let us denote by x the length of the smaller leg of this right-angled triangle.
In the condition of the problem it is said that one leg of this right-angled triangle is 4 more than the other, therefore, the length of the larger leg is x + 4.
It is also known that the hypotenuse of this right-angled triangle is 20, therefore, using the Pythagorean theorem, we obtain the following equation:
x ^ 2 + (x + 4) ^ 2 = 20 ^ 2.
We solve the resulting equation:
x ^ 2 + x ^ 2 + 8x + 16 = 400;
2x ^ 2 + 8x + 16 – 400 = 0;
2x ^ 2 + 8x – 384 = 0;
x ^ 2 + 4x – 192 = 0;
x = -2 ± √ (4 + 192) = -2 ± √196 = -2 ± 14;
x = -2 + 14 = 12.
We find the second leg:
x + 4 = 12 + 4 = 16.
Answer: the legs of this right-angled triangle are 12 and 16.