The length of a rectangle is represented by 4a+3b and its width is represented by 3a-2b. Enter the polynomial for the perimeter of the rectangle. What is the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number?

a) The polynomial for the perimeter of the rectangle is = 14a - 2b

b) 150

Step-by-step explanation:

a) The formula for the area of a rectangle is given as:

P = 2L + 2W

From the question:

The length of a rectangle = 4a+3b

The width of a rectangle = 3a-2b.

The Perimeter of the rectangle is

Perimeter = 2(4a + 3b) + 2(3a - 2b)

Perimeter = 8a + 6b + 6a - 4b

Perimeter = 8a + 6a + 6b - 4b

Perimeter = 14a - 2b

Hence:

The polynomial for the perimeter of the rectangle is = 14a - 2b

b) What is the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number?

Non-zero whole number are single digit number such as: 1, 2, 3, 4, 5, 6, 7, 8, 9

The perimeter of the rectangle is = 14a - 2b

We are asked to find the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number.

In order to solve this, we would used the highest non zero whole number which is 9

Hence,

For a = 12 , b = 9

14 × 12 - 2(9)

= 168 - 18

= 150

Hence, the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number is 150