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 x cm the width of a given rectangle, then (x + 3) cm is its length.

(x * (x + 3)) cm2 is the area of this rectangle. According to the condition of the problem, it is equal to 70 cm2, which means:

x * (x + 3) = 70.

Let’s solve the equation:

x ^ 2 + 3x – 70 = 0.

By Vieta’s theorem:

x1 + x2 = -3,

x1 * x2 = -70, x1 and x2 are the roots of the equation.

By selection, we find that x1 = -10, x2 = 7.

-10 cannot be a solution to the problem, because length rectangle width – non-negative value.

This means that the width of the rectangle is 7 cm, and its length is x + 3 = 7 + 3 = 10 cm.

Answer: length – 10 cm, width – 3 cm.