Question

In $△ABC$, FG and DE are two line segments parallel to BC such that AG=GE=EB. FInd the combined length of DE and FG, if BC=12cm.

Answer 1

Given:

$BC\parallel ED\parallel FG$

$AG=GE=EB$ and $BC=12cm$

Now triangle $\Delta ABC\sim \Delta AFG$...[by $AAA$ criteria]

So,

$\frac{AG}{AB}=\frac{GF}{BC}⟹\frac{1x}{3x}=\frac{GF}{12}⟹GF=4$.

Similarly, triangle $\Delta ABC\sim \Delta AED$...[by $AAA$ criteria]

So,

$\frac{AE}{AB}=\frac{ED}{BC}⟹\frac{2x}{3x}=\frac{ED}{12}⟹ED=8$.

Hence, $DE+FG=4+8=12$ cm.