Find the area of a rectangle if its perimeter is 46 and one side is 5 larger than the other.

The perimeter of the rectangle is found by the formula:

P = 2 * (a + b), where a is its length, b is its width.

According to the conditions of the problem, one side is 5 more than the other, which means the length is 5 more than the width.

The length is expressed in terms of the width.

a = b + 5.

Now we substitute the values into the formula.

46 = 2 * (b + 5 + b).

Divide by 2.

23 = 2 * b + 5.

2 * b = 18.

b = 9, the width of the rectangle.

Let’s find the length of the rectangle.

a = 9 + 5 = 14.

The area of the rectangle is found by the formula:

S = a * b.

Find the area of the rectangle.

S = 14 * 9 = 126 cm2.

Answer: the area of the rectangle is 126 cm2.