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 - Page 437: 39


a. 12 inches b. 1.5 inches

Work Step by Step

You are given that the measurement of the baby's head from top to bottom is 21 inches. By looking at the diagram, you can see that that makes PT=21. You know that PQ + QR + RS + ST = PT. By the extended ratio given, you can determine 4x+x+x+x=21. Solve for x. 7x=21 x=3 Substituting back into the extended ratio gives: PQ=12; QR=3; RS=3; ST=3 The distance from the top of the eyes is $\overline{PQ}$, so the answer is 12 inches. For an adult, you have to look at the extended ratio for an adult, which is given as 4:2:1:1. So, 4x+2x+x+x=21 8x=21 x=$\frac{21}{8}$ You want the distance from the top to the first mark, so: 4x=(4)$\frac{21}{8}$=10.5 Using the answer from question a, you need to subtract. 12-10.5 = 1.5 inches
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