LissyR483721 LissyR483721
  • 25-10-2022
  • Mathematics
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The diagram shows two similar polygonsN51P224048MR3016.5SFigures not drawn to scale.What is the length of CS?

The diagram shows two similar polygonsN51P224048MR30165SFigures not drawn to scaleWhat is the length of CS class=

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FintanV267691 FintanV267691
  • 25-10-2022

Notice the correspondence between the vertices of the polygons:

[tex]VQRGX\approx CNPMS[/tex]

Corresponding segments of similar polygons are proportional. Then:

[tex]\frac{CS}{VX}=\frac{PM}{RG}[/tex]

Substitute VX=48, PM=22 and RG=16.5 and solve for CS:

[tex]\begin{gathered} \Rightarrow\frac{CS}{48}=\frac{22}{16.5} \\ \Rightarrow CS=\frac{22}{16.5}\times48 \\ \Rightarrow CS=64 \end{gathered}[/tex]

Therefore, the length of CS is 64.

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