Find the area of a rectangle if the perimeter is 46 and the other side is 7 larger than the other.

Let’s denote one side of the rectangle by x.

By the condition of the problem, the other side is 7 more than the other, so the other side will be equal to x + 7.

Let’s compose and solve the equation if it is known that the perimeter of the rectangle is 46:

2 (x + x + 7) = 46.

Let’s expand the brackets:

2 x + 2 x + 14 = 46.

4 x = 46 – 14.

4 x = 32.

x = 8.

One side of the rectangle is 8.

Find the other side: 8 + 7 = 15.

Let’s calculate the area of a rectangle by the product of its two sides:

S = 8 * 15 = 120.

Answer: The area of the rectangle is 120.