The length of a rectangle represented by 4a plus 3B and it's width is represented by 3a minus 2b. Write a polynomial for the perimeter of the rectangle. What is the minimum perimeter of the rectangle if a equals 12 and b equals a non zero number?

The polynomial for the perimeter starts from the formula for the perimeter of a rectangle as written below:

Perimeter = 2L + 2W = 2 (L + W)

Perimeter = 2 (4A + 3B + 3A - 2B)

Perimeter = 2 (7A - B)

Let perimeter be P,

P = 14A - 2B - - > this would be the polynomial

Let's substitute A=12 to the polynomial:

P = 14 (12) - 2B = 168 - 2B

To determine the minimum P, set it to 0.0001.

0.0001 = 168 - 2B

B = 83.999 or 84

Thus, the minimum perimeter is achieved if the value of B approached to 84.