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The perimeter of a rectangular ink pad is $34$ centimeters. It is $6$ centimeters tall. How wide is it? $\newline$ $\_\_\_\_$ centimeters

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Area and perimeter: word problems

Full solution

Q. The perimeter of a rectangular ink pad is

34

centimeters. It is

6

centimeters tall. How wide is it?

\newline

\_\_\_\_

centimeters

Identify Formula: Identify the formula for the perimeter of a rectangle. The formula for the perimeter of a rectangle is $P = 2(l + w)$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
Plug in Values: Plug in the known values for $P$ and the height (which can be considered as the length $l$ or the width $w$ in this case) into the formula. $\newline$ Given $P = 34$ centimeters and the height $l = 6$ centimeters, we can write the equation as $34 = 2(6 + w)$ .
Solve for Width: Solve for $w$ . $\newline$ First, divide both sides of the equation by $2$ to isolate the expression with $w$ . $\newline$ $\frac{34}{2} = \frac{2(6 + w)}{2}$ $\newline$ $17 = 6 + w$ $\newline$ Next, subtract $6$ from both sides to solve for $w$ . $\newline$ $17 - 6 = w$ $\newline$ $11 = w$
Verify Solution: Verify the solution. $\newline$ If the width is $11$ centimeters and the height is $6$ centimeters, the perimeter would be $2(6 + 11) = 2(17) = 34$ centimeters, which matches the given perimeter.

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