Certainly! Let's solve this step-by-step.
1. Identify the dimensions of the rectangle:
- Given that the width of the rectangle is [tex]\( x \)[/tex].
- The area of the rectangle is represented by the expression [tex]\( A(x) = x(14 - x) \)[/tex].
- From the area expression, we can see that the length of the rectangle must be [tex]\( 14 - x \)[/tex].
2. Determine the expression for the perimeter:
- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[
P = 2 (\text{width} + \text{length})
\][/tex]
- Here, the width is [tex]\( x \)[/tex] and the length is [tex]\( 14 - x \)[/tex].
- Substituting these values into the formula, we get:
[tex]\[
P = 2 (x + 14 - x)
\][/tex]
3. Simplify the expression:
- Inside the parentheses, [tex]\( x \)[/tex] and [tex]\( -x \)[/tex] cancel each other out:
[tex]\[
P = 2 (14)
\][/tex]
- Simplifying further:
[tex]\[
P = 28
\][/tex]
So the perimeter of the rectangle is [tex]\( 28 \)[/tex].
The correct answer is: A 28
