Question

Write the similarity statement and the scale factor. Then find x, y, and the measure of VU.

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asked 2021-08-09
Write the similarity statement and the scale factor. Then find x, y, and the measure of VU.
Given figure,
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Answers (1)

2021-08-10
In the pentagon ABCDE and pentagon RSTUV
\(\displaystyle\angle{A}=\angle{R}\)
\(\displaystyle\angle{B}=\angle{S}\)
\(\displaystyle\angle{C}=\angle{T}\)
\(\displaystyle\angle{D}=\angle{U}\)
\(\displaystyle\angle{E}=\angle{V}\)
this implies that pentagon ABCDE \(\displaystyle\sim\) pentagon RSTUV
now we have to find scale factor
scale factor \(\displaystyle={\frac{{{C}{D}}}{{{T}{U}}}}={\frac{{{x}}}{{{3}}}}\)
\(\displaystyle\Rightarrow{\frac{{{3}}}{{{2}}}}={\frac{{{x}}}{{{3}}}}\)
\(\displaystyle\Rightarrow{9}={2}{x}\Rightarrow{x}={\frac{{{9}}}{{{2}}}}\)
this is the required answer.
and scale factor \(\displaystyle={\frac{{{D}{E}}}{{{V}{U}}}}\)
\(\displaystyle\Rightarrow{\frac{{{3}}}{{{2}}}}={\frac{{{8}}}{{{y}+{1}}}}\)
\(\displaystyle\Rightarrow{3}{\left({y}+{1}\right)}={16}\)
\(\displaystyle\Rightarrow{3}{y}+{3}={16}\)
\(\displaystyle\Rightarrow{3}{y}={16}-{3}={13}\)
\(\displaystyle\Rightarrow{y}={\frac{{{13}}}{{{3}}}}\)
now, we have to find the value of VY
\(\displaystyle{V}{Y}={y}+{1}={\frac{{{13}}}{{{3}}}}+{1}={\frac{{{13}+{3}}}{{{3}}}}={\frac{{{16}}}{{{3}}}}\)
this is the required answer.
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