The perimeter of the rectangle is 15 cm and its area is 14 cm2. Find the sides of the rectangle.

Let’s compose the system of equations
Let the length be a cm, and the width b cm, we get:
area is the product of length and width, i.e. a * b = 14
the perimeter of the rectangle is the sum of the lengths of all sides, i.e. (a + b) * 2 = 15
compose a system of equations and solve it
a * b = 14
(a + b) * 2 = 15
From the second equation we express the variable a
a = 15/2-b
a = 7.5-b
(7.5-b) * b = 14
7.5b-b ^ 2 = 14, got the quadratic equation
b ^ 2-7.5b + 14 = 0
D = b ^ 2-4ac = 56.25-56 = 0.25, D> 0 two roots
B1 = (7.5-0.5) / 2 = 3.5
B2 = (7.5 + 0.5) / 2 = 4
a = 7.5-b
a = 7.5-3.5 = 4
a = 7.5-4 = 3.5
Answer: 4cm, 3.5cm