Let’s determine the perimeter of Rectangle [tex]\( A \)[/tex] given its dimensions:
Step 1: Identify the length and width of Rectangle [tex]\( A \)[/tex].
- Length = [tex]\( 4x + 5 \)[/tex]
- Width = [tex]\( 3x - 2 \)[/tex]
Step 2: Recall the formula for the perimeter of a rectangle.
The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[ P = 2 \times (\text{Length} + \text{Width}) \][/tex]
Step 3: Substitute the given dimensions into the perimeter formula.
[tex]\[ P = 2 \times ((4x + 5) + (3x - 2)) \][/tex]
Step 4: Simplify the expression inside the parentheses.
[tex]\[ (4x + 5) + (3x - 2) = 4x + 3x + 5 - 2 \][/tex]
[tex]\[ = 7x + 3 \][/tex]
Step 5: Multiply the simplified expression by 2.
[tex]\[ P = 2 \times (7x + 3) \][/tex]
[tex]\[ = 14x + 6 \][/tex]
Therefore, the expression for the perimeter of Rectangle [tex]\( A \)[/tex] is [tex]\( 14x + 6 \)[/tex].
Step 6: Analyze the options provided:
- [tex]\( 14x + 6 \)[/tex]; the answer is a polynomial
- [tex]\( 14x + 6 \)[/tex]; the answer may or may not be a polynomial
- [tex]\( 2x + 6 \)[/tex]; the answer is a polynomial
- [tex]\( 2x + 6 \)[/tex]; the answer may or may not be a polynomial
Correct Option:
[tex]\( 14x + 6 \)[/tex] is indeed a polynomial as it is a linear expression in [tex]\( x \)[/tex]. Therefore, the suitable option that matches the perimeter and acknowledges that it is a polynomial is:
[tex]\( 14x + 6 \)[/tex]; the answer is a polynomial
Thus, the correct answer is [tex]\(\boxed{14x + 6; \text{ the answer is a polynomial}}\)[/tex].
