Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - 7-1 Ratios and Proportions - Practice and Problem-Solving Exercises: 37

Answer

Length is 15 inches; Width is 10 inches

Work Step by Step

The formula for the area of a rectangle is Area=Length x Width You are given the ratio of length to width as 3:2. So, set the length equal to x, and solve for the width. $\frac{3}{2}$=$\frac{x}{w}$ Cross Multiply 3w=2x w=$\frac{2x}{3}$ You are given an area of 150 $in^{2}$, so substitute into the area formula. A=LxW 150=x($\frac{2x}{3})$ 150=$\frac{2x^{2}}{3}$ 450=$2x^{2}$ 225=$x^{2}$ 15=x (this is the length; remember from above we let the length equal x.) Use the proportion to solve for the width. $\frac{l}{w}$=$\frac{3}{2}$ We know the length, so substitute it in for l: $\frac{15}{w}$=$\frac{3}{2}$ Cross Multiply to get width: 3w=15(2) 3w=30 w=10
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