In a rectangle, one side is 2 cm longer than the other; the perimeter is 28 cm, what is the area of this rectangle?

From the condition, we know the perimeter and the fact that one side is 2 cm longer than the other.

Let’s denote by x – the width of the rectangle, then the length will be equal to (x + 2) cm. Substitute them in the formula for finding the perimeter and solve the resulting linear equation with one variable.

(x + x + 2) * 2 = 28;

We divide both sides of the equation by 2 and get an identically equal equation:

x + x + 2 = 14;

We transfer the terms without a variable to the right side:

2x = 14 – 2;

2x = 12;

x = 6.

So, the width of the rectangle is 6 cm, and the length is 6 + 2 = 8 cm.

Calculate the area of ​​the rectangle
Let’s remember the formula for finding the area of ​​a rectangle.

S = a * b, where a and b are the length and width of the rectangle, respectively.

We substitute their values ​​into the formula and calculate the area:

S = 6 * 8 = 48 cm ^ 2.

Answer: 48 cm ^ 2 is the area of ​​a rectangle.