Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 7 - Section 7.2 - Concurrence of Lines - Exercises: 27

Answer

$ RQ = 10 \\ SQ = \sqrt{89} $

Work Step by Step

For an isosceles triangle, the intersection of the perpendicular bisectors of the sides is always a third of the way up the altitude, meaning that RQ is 2/3 of the length of the altitude. We first find the altitude: $h = \sqrt{17^2 - 8^2} = \sqrt{225}=15$ Thus, it follows: $RQ=15(2/3)=10$ We now find SQ. Since RQ equals 10, this means that QZ equals 5. Thus: $SQ = \sqrt{5^2 + 8^2} = \sqrt{89}$
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