The diagonal of the rectangle is 20 cm, and one side is 4 cm larger than the other. Find the sides of the rectangle.

This problem is solved using the Pythagorean theorem, since the length, width and diagonal of the rectangle make up a right-angled triangle. Let the width of the triangle be x cm, then the length is (x + 4) cm.By the Pythagorean theorem, the sum of the squares of the length and width of a rectangle will be equal to the square of the diagonal of this rectangle:
x ^ 2 + (x + 4) ^ 2 = 20 ^ 2;
x ^ 2 + x ^ 2 + 8 * x + 16 – 400 = 0;
2 * x ^ 2 + 8 * x – 384 = 0;
x ^ 2 + 4 * x – 192 = 0.
The roots of this equation are the numbers 12 and -8. The number -8, of course, does not satisfy the condition, since the width cannot be equal to a negative number.
Thus, the width of the rectangle is 12 cm and the length is 16 cm.