Question

6 the length of a rectangle is twice the width w. which expressions represent the perimeter of the rectangle? select all that apply. a. 2w + w + 2w + w b 2w + 2(2w) c 2(w + 2w) d 2(2w) e 6w

Explanation:

Step1: Define length and perimeter formula

Length = $2w$, perimeter = $2(length + width)$

Step2: Check Option A

Sum of all sides: $2w + w + 2w + w = 6w$ (valid)

Step3: Check Option B

$2w + 2(2w) = 2w + 4w = 6w$ (valid)

Step4: Check Option C

$2(w + 2w) = 2(3w) = 6w$ (valid)

Step5: Check Option D

$2(2w) = 4w$ (invalid)

Step6: Check Option E

$6w$ (valid, simplified form)

Answer:

A. $2w + w + 2w + w$, B. $2w + 2(2w)$, C. $2(w + 2w)$, E. $6w$