Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Friday, April 3, 2020

### Geometry Problem 1467: Square, Rectangle, Triangle, Area

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From sim triangles BC/GJ = EB/AG & EB/EA = AG/AB

ReplyDelete=> BC/GJ = EA/AB

NOte that Triangles ABE and EHC are similar ( case AA)

ReplyDeleteso AB/AE=FH/BC => AB.BC=AE.FH

and area (ABCD)= area(FHJG)

AB=s, EB=a, EF=a', FH= s'

ReplyDeleteEA=d=sqrt(s²+a²)=FG

a':a= s:d => a'=as/d

s':a'=s:a => s'=s/a*as/d=s²/d

=> FH*FG=s'*d = s²

Triangle ACE=1/2 of rectangle AJHE, triangle ABE=1/2 of rectangle AGFE. So, triangle ACB=triangle ACE - triangle ABE=1/2(rectangle AJHE - rectangle AGFE) = 1/2 of rectangle FHJG. Again, So, triangle ACB=1/2 of square ABCD. So, rectangle FHJG=square ABCD

ReplyDelete