BdMO National Primary 2015#3

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samiul_samin
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BdMO National Primary 2015#3

Unread post by samiul_samin » Tue Feb 19, 2019 10:29 am

In the following figures a rectangular piece of paper $ABCD$ has been folded several times. First, the side $CD$ was made to fall on the line $AD$. Point $E$ in figure $(ii)$ represents the point $C$ after folding. In the next figure the portion $BF$ was made to fall on $EF$. Lastly, the side $AG$ was made to fall on $GH$. Find the lengths of $GJ, IJ, IE, ED, EH$ and $HF$. It is given that$ AB = 8$ and $BC = 15$.
Screenshot_2019-02-19-10-22-34-1.png
Screenshot_2019-02-19-10-22-34-1.png (22.63 KiB) Viewed 932 times

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samiul_samin
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Re: BdMO National Primary 2015#3

Unread post by samiul_samin » Sat Feb 23, 2019 1:03 pm

According to the given diagram:
$ED=EF=AB=8$
$HF=BF=AE=AD−ED=BC−ED=15−8=7$
$ EH=EF−HF=AB−HF=8−7=1$
$ GJ=GA=EH=1$
$ IJ=EH=1$
$IE=AE−AI=BF−AI=HF−AI=HF−GJ=7−1=6$

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