Okay so Ive figured out half of this question so far, and I need help finding out the rest.

PQRS is an isosceles trapezoid with PS=QR=17 and PQ = 16 and SR = 32. Point R is on SV with RV = 16 and point Q is on the hypotenue ST of right triangle STV. The length of QT is:

a) 26 b) 3 x root of 89 c) 4 x root of 57 d) 3 x root of 93 e) 39

So Ive figured out that the height of the trapezoid is 15

and that QS = root of 801

can someone help me find QT with this information given and explain why ?