Question

If ACDE - AFGE, find the value of x.2740E25DA. O 37.04B. 43.2C44.2D. 48.26

Answer 1

To obtain the value of x, the following steps are necessary:

Step 1: Since both triangles CDE and FGE are similar, the following ratio is valid:

`(EF)/(CE)=(EG)/(DE)`

Step 2: Substitute the value of the lengths of the sides into the ratio as follows:

`\begin{gathered} EF=x \\ CE=27 \\ DE=25 \\ EG=40 \\ \text{Thus:} \\ (EF)/(CE)=(EG)/(DE) \\ \Rightarrow(x)/(27)=(40)/(25) \end{gathered}`

Step 3: Solve the resulting equation for x, as follows:

`\begin{gathered} (x)/(27)=(40)/(25) \\ \Rightarrow x=(40)/(25)*27=(1080)/(25)=43.2 \\ \Rightarrow x=43.2 \end{gathered}`

Therefore, the value of x is 43.2 (Option B)