Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 6

Answer

270 square feet

Work Step by Step

Since the width is stated in terms of the length, we can let l represent the length. The width is 1 more than one-third of the length, which is l, so the width is 1 + $\frac{1}{3}$l. The formula for the perimeter of the rectangle is width + width + length + length The perimeter of the rectangle is 74, so we set up the following equation: l + l + 1 + $\frac{1}{3}$l + 1 + $\frac{1}{3}$l = 74 2l + 2 + $\frac{2}{3}$l = 74 $\frac{6l}{3}$ + 2 + $\frac{2}{3}$l = 74 Subtract 2 from both sides. $\frac{6}{3}$l + $\frac{2}{3}$l = 72 $\frac{8}{3}$l = 72 Divide both sides by $\frac{8}{3}$ l = 72 $\div$ $\frac{8}{3}$ l = 72 $\times$ $\frac{3}{8}$ l = 27 Since the length is 27, the width is 1 + $\frac{1}{3}$ $\times$ 27 = 10. Area= $l \times w$, so we obtain: $A=27 \times 10 = 270 $ square feet.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.