# Given that \triangle FGH is similar to \triangle FED, Calculate DE to the hundedths place.

Given that $$\displaystyle\triangle{F}{G}{H}$$ is similar to $$\displaystyle\triangle{F}{E}{D}$$, Calculate DE to the hundedths place.

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delilnaT
Step 1
Triangle FGH is similar to triangle FED since, angle(F) is common to both the triangles,
and, angle(GHF) = angle(EDF)
and, remaining, angle(HGF) = angle(DEF)
Step 2
So, we have, by the triangle similarity,
$$\displaystyle{\frac{{{D}{E}}}{{{D}{F}}}}={\frac{{{H}{G}}}{{{H}{F}}}}$$
So, $$\displaystyle{\frac{{{D}{E}}}{{{\left({11}+{6}\right)}}}}={\frac{{{4.25}}}{{{8}}}}={0.53125}$$
So, $$\displaystyle{D}{E}={17}\times{0.53125}$$
So, DE=9.03125=9.03
So, DE=9.03