Question

△ghi ~ △efd. find de. de =

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle GHI\sim\triangle EFD\), the ratios of corresponding sides are equal. That is \(\frac{GH}{EF}=\frac{HI}{FD}=\frac{GI}{ED}\). Here, \(GI = 4\), \(HI=2\), \(FD = 1\). Let \(DE=x\). Then \(\frac{GI}{DE}=\frac{HI}{FD}\).

Step2: Substitute the values into the proportion

Substitute \(GI = 4\), \(HI = 2\), \(FD=1\) into \(\frac{GI}{DE}=\frac{HI}{FD}\), we get \(\frac{4}{x}=\frac{2}{1}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(2x=4\times1\). Then \(x = 2\).

Answer:

\(2\)