One side of a rectangle is 4cm smaller than the other. Find the sides of the rectangle if its diagonal is 18cm.

To solve the problem, we will use the Pythagorean theorem, which says that the square of the diagonal is equal to the sum of the squares of the legs.

We take the diagonal of the rectangle as the hypotenuse.

In this case, the first leg will be x cm, the second leg will be: (x – 4) cm.

We get the equation:

x ^ 2 + (x – 4) ^ 2 = 18 ^ 2.

x ^ 2 + x ^ 2 – 8 * x + 16 = 324.

2 * x ^ 2 – 8 * x – 308 = 0.

x ^ 2 – 4 * x – 154 = 0.

D ^ 2 = (-4) ^ 2 – 4 * 1 * (-154) = 16 + 616 = 634.

D = 25.13.

x1 = (-4 + 25.13) = 10.57 cm (first side).

x2 = (4 + 25.13) / 2 = 14.59 cm (second side).

Answer: 10.57 and 14.59 cm.