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