The width of the rectangle is 6 cm less than the length, and the area is 40 cm ^ 2. Find the sides of the rectangle.

Let’s denote by x the length of this rectangle.
According to the condition of the problem, the width of this rectangle is 6 cm less than its length, therefore, the width of this rectangle is x – 6 cm.
It is also known that the area of ​​this rectangle is 40 cm², therefore, we can draw up the following equation:
x * (x – 6) = 40.
We solve the resulting equation:
x² – 6x – 40 = 0;
x = 3 ± √ (9 + 40) = 3 ± √49 = 3 ± 7;
x1 = 3 + 7 = 10;
x2 = 3 – 7 = -4.
Since the length of the side of the rectangle is positive, the value x = -4 is not suitable.
Knowing the length of this rectangle, we find its width:
10 – 6 = 4 cm.

Answer: the lengths of the sides of this rectangle are 10 cm and 4 cm.