The perimeter of the rectangle is 28m, and its area is 40m2. Find the sides of the rectangle.

We denote the sides of the rectangle by x and y m.

Let’s write down the formulas for the perimeter and area for a given rectangle:

(x + y) * 2 = 28,

x * y = 40.

Let us express x in this equation through y and substitute it into the second equation:

(x + y) * 2 = 28;

x + y = 28: 2;

x + y = 14;

x = 14 – y.

The second equation after substitution is:

(14 – y) * y = 40;

14y – y ^ 2 – 40 = 0;

– y ^ 2 + 14y – 40 = 0;

D = 14 ^ 2 – 4 * (-1) * (-40) = 196 – 160 = 36;

x1 = (-14 + √36) / (2 * (-1)) = (-14 + 6) / (- 2) = -8 / (- 2) = 4;

x2 = (-14 – √36) / (2 * (-1)) = (-14 – 6) / (- 2) = -20 / (- 2) = 10.

y1 = 14 – 4 = 10;

y2 = 14 – 10 = 4.

Answer: The sides of the rectangle are 4 m, 10 m, 4 m, 10 m.