The length of the rectangle is 2 cm more than the width. If you increase the length of the side by 4 cm

The length of the rectangle is 2 cm more than the width. If you increase the length of the side by 4 cm, then the area of the rectangle will become even 48 cm2. What are the lines of a rectangle?

1. It is known that the area of ​​a rectangle is equal to the product of its length and width.

2. Let’s designate the length as x cm.

Then, by the condition of the problem, the width is 2 cm less and equal to (x – 2) cm.

3. Let us write the equation for the area S of the resulting rectangle, if it is known that it is equal to 48 square centimeters.

S = (x + 4) * (x – 2 + 4) = 48 cm ^ 2;

x ^ 2 + 4 x + 2 x + 8 = 48;

x ^ 2 + 6 x – 40 = 0;

Let’s solve the quadratic equation:

x = {- 6 + (36 + 160): 1/2}: 2 = (- 6 +14): 2 = 4 centimeters.

We know that the width is 2 cm less, which means it is 4 cm – 2 cm = 2 centimeters.

Answer: The length of the rectangle is 4 centimeters, the width is 2 centimeters