What are the sides of a rectangle if its perimeter is 26 cm and its area is 30 cm2?

To solve the problem, it is necessary to compose a system of equations in which we write the length of the rectangle as x cm, and the width as y cm.
In this case, the perimeter of the rectangle will be:
2 * (x + y) = 26 cm.
x + y = 13 cm.
x = 13 – y.

We write the area of the rectangle as:
x * y = 30 cm.

Substitute the x value from the first equation into the second.
(13 – y) * y = 30.
13 * y – y2 = 30.
y2 – 13 * y + 30 = 0.
We find the value of y.
D = 13 * 13 – 4 * 1 * 30 = 169 – 120 = 49.
y = 7.

Substitute the value for y in the first equation:
x = 13 – 7 = 6 cm.

Answer: 6 and 7 cm.