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Licemer1 [7]
3 years ago
6

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

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.

\frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU}..........(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:

\frac{y}{22}=\frac{8}{20}=\frac{5}{x+3}

Now, as can be clearly seen, to find y we will use the first two ratios as:

\frac{y}{22}=\frac{8}{20}

y=\frac{8\times 22}{20}=8.8

In a similar manner, to find the value of x we can use the last two ratios:

\frac{8}{20}=\frac{5}{x+3}

After cross multiplication we get:

5\times 20=8(x+3)

Which can be simplified as:

x+3=\frac{100}{8} =12.5

Thus, x=12.5-3=9.5

Therefore, the required answer is:

x=9.5 and y=8.8



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