# The perimeter of the square is 8 cm. Find the sum of the sides of an equal rectangle if one of its sides

**The perimeter of the square is 8 cm. Find the sum of the sides of an equal rectangle if one of its sides is 3 cm larger than the other.**

We will solve this task in steps and explain each of them in detail.

1) 8: 4 = 2 centimeters – the length of the side of the square, since its perimeter is 8 centimeters;

2) 2 * 2 = 4 cm ^ 2 – the area of a square with a side of 2 centimeters;

3) Let the length of the rectangle be x centimeters, then the width of the rectangle is (x + 3) centimeters. We know that its area is 4 cm ^ 2. Let’s make the equation:

x * (x + 3) = 4;

x ^ 2 + 3x – 4 = 0;

a = 1, b = 3, c = -4;

D = b ^ 2 – 4 * a * c = 9 + 16 = 25 (the discriminant is greater than zero, then this quadratic equation has two roots);

x = (-b + √ D) / 2 * a = (-3 + √ 25) / 2 * 1 = (-3 + 5) / 2 * 1 = 2/2 = 1;

x = (-b – √ D) / 2 * a = (-3 – √ 25) / 2 * 1 = (-3 – 5) / 2 * 1 = -4 does not satisfy the condition of the problem;

1 + 3 = 4 centimeters;

(4 + 1) * 2 = 5 * 2 = 10 centimeters.

Answer: 10 centimeters.