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The perimeter of a rectangular closet is $18\,\text{feet}$ . It is $4\,\text{feet}$ wide. How long is it? $\newline$ $\_\_\_\_\_$ feet

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Area and perimeter: word problems

Full solution

Q. The perimeter of a rectangular closet is

18\,\text{feet}

. It is

4\,\text{feet}

wide. How long is it?

\newline

\_\_\_\_\_

feet

Identify Formula: Identify the formula for the perimeter of a rectangle. $\newline$ The formula for the perimeter of a rectangle is $P = 2l + 2w$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
Plug in Values: Plug in the values of $P$ and $w$ into the formula. $\newline$ Given $P = 18$ feet and $w = 4$ feet, we can substitute these values into the formula to get $18 = 2l + 2(4)$ .
Simplify Equation: Simplify the equation. $\newline$ $18 = 2l + 8$ can be simplified by subtracting $8$ from both sides to isolate the term with $l$ . $\newline$ $18 - 8 = 2l$ $\newline$ $10 = 2l$
Solve for l: Solve for l. $\newline$ Divide both sides of the equation by $2$ to solve for l. $\newline$ $\frac{10}{2} = \frac{2l}{2}$ $\newline$ $5 = l$

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