Question

Find the value of x that makes ADEF ~AXYZ..yE1052x – 114D11FX5x + 2Zх=

Answer 1

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.

`\begin{gathered} (XY)/(DE)=(YZ)/(EF) \\ (10)/(5)=(14)/(2x-1) \end{gathered}`

Now, we solve for x

`\begin{gathered} 2=(14)/(2x-1) \\ 2x-1=(14)/(2) \\ 2x=7+1 \\ x=(8)/(2) \\ x=4 \end{gathered}`

Hence, the answer is x = 4.