The area of the rectangle is 480 dm2. Find its sides if the perimeter of the rectangle is 94 dm.

Let us denote the lengths of the sides of this rectangle through x and y.

According to the condition of the problem, the area of ​​this rectangle is 480 dm ^ 2, therefore, we can draw up the following equation:

x * y = 480.

It is also known that the perimeter of this rectangle is 94 dm, therefore, we can draw up the following equation:

2 * (x + y) = 94.

We solve the resulting system of equations.

From the second equation we find:

x + y = 94/2;

x + y = 47;

y = 47 – x.

Substituting this value y = 47 – x into the equation x * y = 480, we get:

x * (47 – x) = 480;

47x – x ^ 2 = 480:

x ^ 2 – 47x + 480 = 0;

x = (47 ± √ (47 ^ 2 – 4 * 480)) / 2 = (47 ± √ (2209 – 1920)) / 2 = (47 ± √289) / 2 = (47 ± 17) / 2;

x1 = (47 – 17) / 2 = 15;

x2 = (47 + 17) / 2 = 32.

We find at:

y1 = 47 – x1 = 47 – 15 = 32;

y2 = 47 – x2 = 47 – 32 = 15.

Answer: the sides of this rectangle are 15 inches and 32 inches.