Geometry: Common Core (15th Edition)

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

Chapter 1 - Tools of Geometry - 1-3 Measuring Segments - Practice and Problem-Solving Exercises - Page 24: 14


a) y=7 b) RS=60, ST=36, RT=96

Work Step by Step

According to the Segment Addition Postulate, $RS+ST=RT$. We substitute the values of RS, ST, and RT into the equation to get :$8y+4+4y+8=15y-9$. Combining like terms gives: $$12y+12=15y-9 \\ -3y=-21 \\ y=7$$. To find RS, ST, and RT, we substitute 7 in for any occurrence of y. For RS, $8y+4=8(7)+4=56+4=60$. For ST, $4y+8=4(7)+8=28+8=36$. For RT, $15y-9=15(7)-9=105-9=96$
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