## Elementary Geometry for College Students (5th Edition)

$RQ = 10 \\ SQ = \sqrt{89}$
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: $SQ = \sqrt{5^2 + 8^2} = \sqrt{89}$