# A rectangle has one side 2 cm longer than the other, and the perimeter is 28 cm. What is the area of this rectangle?

January 28, 2021 | education

| A rectangle is a rectangle whose opposite sides are parallel and equal in pairs.

The side of the rectangle that is longer is called the length, and the side that is shorter is called the width.

Suppose, by condition, a rectangle is given whose width is b, then its length is b + 2, since by condition it is 2 cm longer.

1. The perimeter of the rectangle is:

P = a + b + a + b = 2 * a + 2 * b = 2 * (a + b),

where a – length, b – width.

Substitute the data for the value condition:

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

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

4 * (b + 1) = 28;

b + 1 = 28/4;

b + 1 = 7;

b = 7 – 1;

b = 6 cm.

Find the length:

a = 6 + 2 = 8 (cm).

2. The area of the rectangle is:

S = a * b = 8 * 6 = 48 (cm²).

Answer: S = 28 cm².

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