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The perimeter $p$ of the rectangle below is $30$ inches. Which formula can be used to find the length and width of the rectangle? $\newline$ A $p = w + (w + 3)$ $\newline$ B $p = w(w + 3)$ $\newline$ C $p = 2w + 2(w + 3)$ $\newline$ D $p = 2(w + 3) - 2w$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The perimeter

p

of the rectangle below is

30

inches. Which formula can be used to find the length and width of the rectangle?

\newline

A

p = w + (w + 3)

\newline

B

p = w(w + 3)

\newline

C

p = 2w + 2(w + 3)

\newline

D

p = 2(w + 3) - 2w

Identify Formula: Identify the correct formula for the perimeter of a rectangle. $\newline$ The perimeter $P$ of a rectangle is given by $P = 2(\text{length} + \text{width})$ . $\newline$ Here, the width is $w$ and the length is $w + 3$ . $\newline$ So, the formula becomes $P = 2(w + (w + 3))$ .
Match with Options: Match the derived formula with the given options. $\newline$ The derived formula is $P = 2(w + w + 3) = 2(2w + 3)$ . $\newline$ Simplify to get $P = 4w + 6$ . $\newline$ Compare with options: $\newline$ A) $p = w + (w + 3)$ - Incorrect, doesn't account for all sides. $\newline$ B) $p = w(w + 3)$ - Incorrect, represents area, not perimeter. $\newline$ C) $p = 2w + 2(w + 3)$ - Correct, simplifies to $4w + 6$ . $\newline$ D) $p = 2(w + 3) – 2w$ - Incorrect, simplifies to $6$ .

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