Question

A rectangle has an area of 24 square inches. If the side

lengths of the rectangle are integers, which of the
following could be the perimeter of this rectangle?

Answer 1

Possible perimeters:

50 inches, 28 inches, 22 inches, 20 inches.

Explanation:

Given that:

Area of triangle = 24 square inches

Side lengths of rectangle are integers.

To find:

Possible perimeter of this rectangle = ?

Solution:

Here, options are missing, so let us calculate all possibilities for the perimeter.

The formula for Area of a rectangle is given as:

`A = Length * Width`

Let us make integer factors of 24 first of all.

`24 = 1 * 24\\24 = 2 * 12\\24 = 3 * 8\\24 = 4 * 6`

These are the four possibilities of length and breadth.

Let us calculate the possible perimeter for each case using the formula for perimeter:

`Perimeter = 2* (Length + Width)`

1st possible option:

`Perimeter = 2* (1+ 24) = 50\ inches`

2nd possible option:

`Perimeter = 2* (2+ 12) = 28\ inches`

3rd possible option:

`Perimeter = 2* (3+ 8) = 22\ inches`

4th possible option:

`Perimeter = 2* (4+ 6) = 20\ inches`