Question

1. reason the length of a rectangle is represented by 4 + 6x. the width is half the length. what expression represents the perimeter of this rectangle? explain your reasoning.

Explanation:

Step1: Find the width expression

The length \( l = 4 + 6x \). The width \( w \) is half the length, so \( w=\frac{1}{2}(4 + 6x)=2 + 3x \).

Step2: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \).

Step3: Substitute length and width into formula

Substitute \( l = 4 + 6x \) and \( w = 2 + 3x \) into the formula:

$$
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$$

Answer:

The expression for the perimeter is \( 12 + 18x \)