如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,AD=12cm,矩形FGHI的周

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如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,AD=12cm,矩形FGHI的周如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,

如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,AD=12cm,矩形FGHI的周
如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,AD=12cm,矩形FGHI的周

如图,△ABC中,AD⊥BC于D,FGHI为矩形,FG/GH=5/9BC=36cm,AD=12cm,矩形FGHI的周
∵FI∥GH,
∴△AFI∽△ABC,
∵AD⊥BC于D,
∴AE⊥FI,
∴AE/AD=FI/BC ①,
设FG=5X,则DE=FG=5X,FI=GH=9X,
∴AE=AD-DE=12-5X
代入①得(12-5X)/12=9X/36
解得X=1.5,
∴周长=2*(5X+9X)=42 cm