What are the sides of a rectangle in which one side is 9 cm larger than the other and the area is 252 cm2.

Let’s write one of the sides of the rectangle equal to x cm.
We know that the second side is 9 cm larger than the first, so its value will be: x + 9 cm.
Since the area is the product of the sides of the rectangle, we get the equation:
x * (x + 9) = 252.
x ^ 2 + 9 * x = 252.
x ^ 2 + 9 * x – 252 = 0.
D ^ 2 = 9 * 9 – 4 * 1 * (-252) = 81 + 1008 = 1089.
D = √1089 = 33.
x = (-9 + 33) / 2 = 24/2 = 12 cm (first side).
x + 9 = 12 + 9 = 21 cm (second side).
Answer: the sides of the rectangle are 12 and 21 cm.