Question

1. if \\( \triangle c d e \sim \triangle f g e \\), find the value of \\( x \\).

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle CDE\) and \(\triangle FGE\), the ratios of corresponding sides are equal. So, \(\frac{CD}{FG}=\frac{DE}{FE}\).

Step2: Substitute the known values

We know \(CD = 27\), \(FG=40\), \(DE = 25\), and \(FE=x\). Substituting these into the proportion \(\frac{27}{40}=\frac{25}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(27x=25\times40\).

Step4: Solve for \(x\)

First, calculate \(25\times40 = 1000\). Then \(x=\frac{1000}{27}\approx37.04\).

Answer:

\(x=\frac{1000}{27}\)