The area of the rectangle is 14 cm2, the perimeter is 18 cm. Find the measurement of the rectangle.

Let’s denote the side of the rectangle through a, the second side through b. The area is equal to the product of the opposite sides. We get the following.
S = a × b.
a × b = 14.
The perimeter is the sum of the lengths of all sides.
P = (a + b) × 2.
(a + b) × 2 = 18.
We express the value of a from the first expression.
a = 14 / b.
(14 / b + b) × 2 = 18.
14 / b + b = 18 ÷ 2.
14 / b + b = 9.
14 + b ^ 2 – 9 b = 0.
B ^ 2 – 9 b + 14 = 0.

D = 81-4 * 14 = 25, b1 = (9 + 5) / 2 = 7 b2 = (9-5) / 2 = 2, so a = 9-7 = 2; a = 9 – 2 = 7.
Answer: the sides are 2 and 7 cm, 9 and 2 cm.