Question

The area of a rectangle is 42 square feet.

If the length and width are whole numbers, what are the least and greatest possible
perimeters?
26 ft. and 34 ft.
34 ft. and 86 ft.
26 ft. and 86 ft.
42 ft. and 84 ft.​

Answer 1

26 ft and 46 ft.

Explanation:

The prime factors of 42 are 2 * 3 * 7.

Possible lengths and widths are:

L = 7, W = 6 giving a perimeter of 2*7 + 2*6 = 26 ft.

L = 14 , W = 3 giving perimeter = 34 ft.

L = 21, W = 2 giving perimeter = 46 ft.