Question 1154273
<pre>
{{{drawing(400,4200/13,-1,12,-1,9.5,

line(0,0,2.8125,8.549259836), 
line(0,0,8,0),
line(8,0,10.8125,8.549259836),
line(10.8125,8.549259836,2.8125,8.549259836),
locate(5,5.5,T),
locate(0,0,P),locate(8,0,Q),locate(10.8,9.1,R),locate(2.8,9.1,S),

line(0,0,7.8125,8.549259836), locate(7.9,9.1,F), line(8,0,2.8125,8.549259836),

locate(4,0,8), locate(5,9.1,5), locate(1,4.5,9), locate(9,4.5,9),
locate(4,7,"?"), locate(6.2,3.5,"?")


 )}}}

ΔFST ∽ ΔPQT

{{{(PQ)/(FS)=(TQ)/(TS)}}}

{{{(8)/(5)=(TQ)/(TS)}}}

{{{TS + TQ = QS = 8}}}

{{{TS + TQ = 8}}}

{{{TQ = 8-TS}}}

{{{(8)/(5)=(8-TS)/TS}}}

Cross-multiply:

{{{8*TS=5(8-TS)}}}

Distribute:

{{{8*TS=40-5*TS}}}

{{{13*TS=40}}}

{{{TS=40/13}}}

Substitute in

{{{TQ = 8-TS}}}

{{{TQ = 8-40/13}}}

Get LCD

{{{TQ = 104/13-40/13}}}

{{{TQ=64/13}}}

Answer: 
{{{TQ=64/13=4&12/13}}}
{{{TS=40/13=3&1/13}}}

Edwin</pre>