# To determine: The value of segment HF Given information: The following information has been given EH=7 HG=4

Question
Similarity
To determine: The value of segment HF
Given information:
The following information has been given
EH=7
HG=4

2020-11-21
Formula used:
Similar triangles have sides in same ratio.
Calculation:
We know that in similar triangles HFE and FGE,
$$\displaystyle\frac{{{H}{F}}}{{{F}{G}}}=\frac{{{F}{E}}}{{{G}{E}}}=\frac{{{H}{E}}}{{{F}{E}}}$$(by law of similarity)
Hence, we substitute the value of EH and HG in the equation above , we get
$$\displaystyle{F}{E}^{{2}}={H}{E}{\left({G}{E}\right)}$$
Thus, we get
$$\displaystyle{F}{E}=\sqrt{{{77}}}$$

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