Answer:
a) The polynomial for the perimeter of the rectangle is = 14a - 2b
b) 150
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