JailynneI331508 JailynneI331508
  • 25-10-2022
  • Mathematics
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Find the value of x that makes ADEF ~AXYZ..yE1052x – 114D11FX5x + 2Zх=

Find the value of x that makes ADEF AXYZyE1052x 114D11FX5x 2Zх class=

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MackenzeeD497279 MackenzeeD497279
  • 25-10-2022

Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.

[tex]\begin{gathered} \frac{XY}{DE}=\frac{YZ}{EF} \\ \frac{10}{5}=\frac{14}{2x-1} \end{gathered}[/tex]

Now, we solve for x

[tex]\begin{gathered} 2=\frac{14}{2x-1} \\ 2x-1=\frac{14}{2} \\ 2x=7+1 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]

Hence, the answer is x = 4.

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