Find the area of a rectangle if its perimeter is 44 and one side is 2 larger than the other.

1) Find the sides of the rectangle. Let’s write the formula for the perimeter:
P = (a + b) × 2, where a is the length of the rectangle, b is the width.
It is known that one side of a rectangle is 2 larger than the other, which means:
a = b + 2,
We substitute the values of the sides into the formula for the perimeter:
P = ((b + 2) + b) × 2 = (b + 2 + b) × 2 = (2b + 2) × 2 = 4b + 4,
44 = 4b + 4,
44-4 = 4b,
4b = 40,
b = 10.
Find side a:
a = 10 + 2 = 12
2) The area of the rectangle is calculated by the formula:
S = a × b,
S = 12 × 10 = 120 sq. Units
Answer: the area of the rectangle is 120 square units.