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Question Number 210695 by cherokeesay last updated on 16/Aug/24

Commented by A5T last updated on 17/Aug/24

Answered by mr W last updated on 17/Aug/24

Commented by mr W last updated on 17/Aug/24

$$thenumbersinthefiguremeanthe$$$$ratiosofthecorrespondingsegments,$$$$i.e.1:3,1:a:b.$$$$wehave$$$$\frac{1}{a}\times \frac{a}{b}\times \frac{4}{1}=1\Rightarrow b=4$$$$\frac{1}{a+b}\times \frac{3}{1}\times \frac{4}{1}=1\Rightarrow a+b=12\Rightarrow a=8$$$$\left[ABE\right]=\frac{1}{4}\left[ABC\right]$$$$\left[AHE\right]=\frac{1}{1+a+b}\times \left[ABE\right]=\frac{1}{13}\times \frac{1}{4}\left[ABC\right]=\frac{1}{52}\left[ABC\right]$$$$\left[HFG\right]=\left[ABC\right]-3\times \frac{1}{4}\left[ABC\right]+3\times \frac{1}{52}\left[ABC\right]$$$$=\frac{7}{26}\left[ABC\right]=\frac{7}{26}\times 26=7✓$$

Commented by cherokeesay last updated on 17/Aug/24

$$sonice!thankyousir!$$

Commented by cherokeesay last updated on 17/Aug/24

$$thankyou!$$

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