Question

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

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

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 $$\displaystyle={\frac{{{C}{D}}}{{{T}{U}}}}={\frac{{{x}}}{{{3}}}}$$
$$\displaystyle\Rightarrow{\frac{{{3}}}{{{2}}}}={\frac{{{x}}}{{{3}}}}$$
$$\displaystyle\Rightarrow{9}={2}{x}\Rightarrow{x}={\frac{{{9}}}{{{2}}}}$$
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
$$\displaystyle{V}{Y}={y}+{1}={\frac{{{13}}}{{{3}}}}+{1}={\frac{{{13}+{3}}}{{{3}}}}={\frac{{{16}}}{{{3}}}}$$