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.