The width of the rectangle is 3 cm less than the length and the area is 70 cm2.

The width of the rectangle is 3 cm less than the length and the area is 70 cm2. Find the lengths of 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 3 cm less than the length, therefore, the width of this rectangle is:
x – 3 cm.
It is also known that the area of ​​this rectangle is 70 cm², therefore, we can draw up the following equation:
x * (x – 3) = 70.
We solve the resulting equation:
x² – 3 * x = 70;
x² – 3 * x – 70 = 0;
x = (3 ± √ (3² + 4 * 70)) / 2 = (3 ± √ (9 + 280)) / 2 = (3 ± √289) / 2 = (3 ± 17) / 2;
x1 = (3 – 17) / 2 = -14 / 2 = -7;
x2 = (3 + 17) / 2 = 20/2 = 10.
Since the length of the side of the rectangle is positive, the value x = -7 is not suitable.
Knowing the length of this rectangle, we find its width:
x – 3 = 10 – 3 = 7 cm.

Answer: the lengths of the sides of this rectangle are 10 cm and 7 cm.