The sum of the length and two widths of the rectangle is 16 cm, find the sides of the rectangle if the area is 30 cm2.

Let us denote the length of this rectangular quadrangle by a, and the width of this rectangular quadrilateral by b.

In the initial data for this task, it is reported that if we add two widths and one length of this quadrangle, then the result will be 16, therefore, the following relation holds:

a + 2b = 16.

It is also known that the area of ​​this rectangular quadrangle is 30 cm ^ 2, therefore, the following relationship holds:

a * b = 30.

We solve the resulting system of equations.

Substituting into the second equation the value a = 16 – 2b from the first equation, we get:

(16 – 2b) * b = 30;

16b – 2b ^ 2 = 30;

b ^ 2 – 8b + 15 = 0;

b = 4 ± √ (16 – 15) = 4 ± √1 = 4 ± 1;

b1 = 4 + 1 = 5;

b2 = 4 – 1 = 3.

We find a:

a1 = 16 – 2 * 5 = 26 – 10 = 6;

a2 = 16 – 2 * 3 = 26 – 6 = 10.

Answer: the lengths of the sides can be 5 cm and 6 cm or 3 cm and 10 cm.