Answer :
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-2
WU=WV+VU=12+8=20
TU=5
SU=ST+TU=(x-2)+5=x+3
Thus, 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