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The perimeter of a rectangular piece of paper is $46$ inches. The paper is $8$ inches wide. How long is it? $\newline$ $\_\_\_\_$ inches

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Area and perimeter: word problems

Full solution

Q. The perimeter of a rectangular piece of paper is

46

inches. The paper is

8

inches wide. How long is it?

\newline

\_\_\_\_

inches

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 $P = 2l + 2w$ . We know $P = 46$ inches and $w = 8$ inches, so we replace these values in the formula: $46 = 2l + 2(8)$
Simplify Equation: Simplify the equation by performing the multiplication. $46 = 2l + 16$
Isolate Term: Isolate the term with $l$ by subtracting $16$ from both sides of the equation. $46 - 16 = 2l$ $30 = 2l$
Solve for $l$ : Solve for $l$ by dividing both sides of the equation by $2$ . $\frac{30}{2} = \frac{2l}{2}$ $15 = l$
State Length: State the length of the rectangular piece of paper. $\newline$ The length of the paper is $15$ inches.

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