Question

The length and width of a rectangle are whole numbers of centimeters. Neither is divisible by 6. The area of the rectangle is 36 square centimeters.what is the perimeter of the rectangle, in centimeters?

Answer 1

For this case we have:

The area of a rectangle is given by:
`A = a * b`

Where "a" is the largest side

"b" is the minor side

On the other hand, the perimeter is given by:

`P = 2a + 2b`

If we have:

`A = a * b\\36 = a * b`

We must look for two whole numbers not divisible by 6, that when multiplied give 36.

`6 * 6 = 36`, but 6 is divisible by 6

`18 * 2 = 36`, but 18 is divisible by 6

`12 * 3 = 36`, but 12 is divisible by 6

We know that
`9 * 4 = 36`, 9 or 4 are divisible by 6.

`a = 9\\b = 4`

Thus, the perimeter is given by:

`P = 2 (9) +2 (4)\\P = 18 + 8\\P = 26cm`

Answer:

26cm