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