The perimeter of the rectangle is 28 cm and its area is 45 cm2. Find the sides of the rectangle.

1. Let X be one side of the rectangle and Y the other side.

2. Then, based on the condition, X * Y = 45, and X + X + Y + Y = 2X + 2Y = 28.

3. So 2 * (X + Y) = 28, and X + Y = 14. We get that X = 14 – Y.

4. Substituting the value of X into the equation X * Y = 45, we find (14 – Y) * Y = 45.

5.14Y – Y2 = 45, and Y2 – 14Y + 45 = 0.

6. Using the formula for the roots of the quadratic equation, we find that Y = (14 + 4) / 2 = 9 and Y = (14 – 4) / 2 = 5.

7. If one side is 5 cm, then the other is 45: 5 = 9 cm and vice versa.