Find x and y, given that line WS and line VT are parallel. Show all work!

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.[tex] \frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU} [/tex]..........(Equation 1)Checking the diagram given, we see that:VT=y, WS=22, VU=8, ST=x-2WU=WV+VU=12+8=20TU=5SU=ST+TU=(x-2)+5=x+3Thus, substituting the required values in (Equation 1) we get:[tex] \frac{y}{22}=\frac{8}{20}=\frac{5}{x+3} [/tex]Now, as can be clearly seen, to find y we will use the first two ratios as:[tex] \frac{y}{22}=\frac{8}{20} [/tex][tex] y=\frac{8\times 22}{20}=8.8 [/tex]In a similar manner, to find the value of x we can use the last two ratios:[tex] \frac{8}{20}=\frac{5}{x+3} [/tex]After cross multiplication we get:[tex] 5\times 20=8(x+3) [/tex]Which can be simplified as:[tex] x+3=\frac{100}{8} =12.5 [/tex]Thus, [tex] x=12.5-3=9.5 [/tex]Therefore, the required answer is:x=9.5 and y=8.8