Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 4 - An Introduction to Functions - Cumulative Test Prep - Gridded Response - Page 288: 20


110 ft

Work Step by Step

First lets find the length of Rectangle A. We know that the area of that rectangle is 180 square ft or also Length $\times$ Width. The width is 20 so the length is 90 because that is the only number that when you multiply with 20, you get 180. Now, we can find the perimeter of Rectangle A. The perimeter formula is: Perimeter=(2$\times$Length)+(2$\times$Width) When we plug the width and length of the Rectangle A into this formula, we get 220 feet as our perimeter of Rectangle A. Now lets find the proportion of the areas of the two rectangles: $\frac{Rectangle-A}{Rectangle-B}$ = $\frac{180}{45}$=$\frac{4}{1}$ We know that the square of the ratios of the perimeters of similar figures is the ratio of their areas so lets take the square root of this ratio to find the ratio of their perimeters. $\sqrt\frac{4}{1}$=$\frac{2}{1}$ So if the perimeter of Rectangle A is 220 ft and the ratio of the perimeter of Rectangle A to Rectangle B is 2 to 1, the perimeter of Rectangle B is 110 ft.
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