"Write the similarity statement and the scale factor...." was answered by students like you

bobbie71G

Answered question

2021-08-09

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

Anonym

Skilled2021-08-10Added 108 answers

In the pentagon ABCDE and pentagon RSTUV

∠ A = ∠ R

∠ B = ∠ S

∠ C = ∠ T

∠ D = ∠ U

∠ E = ∠ V

this implies that pentagon ABCDE

\sim

pentagon RSTUV
now we have to find scale factor
scale factor

= \frac{C D}{T U} = \frac{x}{3}

\Rightarrow \frac{3}{2} = \frac{x}{3}

\Rightarrow 9 = 2 x \Rightarrow x = \frac{9}{2}

this is the required answer.
and scale factor

= \frac{D E}{V U}

\Rightarrow \frac{3}{2} = \frac{8}{y + 1}

\Rightarrow 3 (y + 1) = 16

\Rightarrow 3 y + 3 = 16

\Rightarrow 3 y = 16 - 3 = 13

\Rightarrow y = \frac{13}{3}

now, we have to find the value of VY

V Y = y + 1 = \frac{13}{3} + 1 = \frac{13 + 3}{3} = \frac{16}{3}

this is the required answer.

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