Question

Find x.HF 9FD 12DG 9HG 6EG x+5

Answer 1

In this case triangle EHG is a similar triangle with EFD, and it must have a scale factor.

Since we have side FD and the similar side HG we can find the scale factor

`\begin{gathered} kFD=(HG) \\ 12k=6 \\ k=(1)/(2) \end{gathered}`

in this case we found that the inner triangle is going to be half of the triangle of the ouside, and that all the sides must become half, meaning that side EH also has to be 9.

Also we know that it is an isosceles triangle and the sides different from the base have to be equal, meaning that

`\begin{gathered} EH=EG \\ 9=x+5 \\ x=9-5 \\ x=4 \end{gathered}`