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Exercises Equations and inequalities

Example 4 from Algebra and Trigonometry, 2.3 Models and Applications

Solving a Perimeter Problem

The perimeter of a rectangular outdoor patio is $54$ ft. The length is $3$ ft greater than the width. What are the dimensions of the patio?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The perimeter formula is standard: $P = 2 L + 2 W .$ We have two unknown quantities, length and width. However, we can write the length in terms of the width as $L = W + 3.$ Substitute the perimeter value and the expression for length into the formula. It is often helpful to make a sketch and label the sides as in Figure 3.

Figure 3

Now we can solve for the width and then calculate the length.

$\begin{matrix} P & = & 2 L + 2 W \\ 54 & = & 2 (W + 3) + 2 W \\ 54 & = & 2 W + 6 + 2 W \\ 54 & = & 4 W + 6 \\ 48 & = & 4 W \\ 12 & = & W \\ (12 + 3) & = & L \\ 15 & = & L \end{matrix}$

The dimensions are $L = 15$ ft and $W = 12$ ft.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the dimensions of a rectangle given that the perimeter is $110$ cm and the length is 1 cm more than twice the width.

How did it go?

PreviousSolving an Application Using a Formula Next Solving an Area Problem

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.