Question

perimeter of a rectangle the perimeter of the rectangle is 32 cm. the length is 1 cm more than twice the width. let the width be represented by the variable w. which of the following represents the length? options: w + 2, 2w + 1, w - 2, 2w - 1 label the remaining sides of the rectangle. rectangle image with width labeled w

Explanation:

Step1: Analyze the relationship between length and width

The problem states that the length is 1 cm more than twice the width. Let the width be \( w \). Twice the width is \( 2w \), and 1 cm more than that is \( 2w + 1 \). So the length should be represented by the expression \( 2w + 1 \).

To label the remaining sides of the rectangle, we know that in a rectangle, opposite sides are equal. So if one side (width) is \( w \), the opposite side is also \( w \). And if the length is \( 2w + 1 \), the opposite side (the other length) is also \( 2w + 1 \).

Step2: Confirm the length expression

From the given options, the expression \( 2w + 1 \) matches our derived expression for the length. So we label the longer sides (lengths) of the rectangle with \( 2w + 1 \) and the shorter sides (widths) with \( w \).

Answer:

The length is represented by \( 2w + 1 \). The remaining sides: the two width sides are labeled \( w \) and the two length sides are labeled \( 2w + 1 \).