Friday, April 3, 2020

Geometry Problem 1467: Square, Rectangle, Triangle, Area

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1467: Square, Rectangle, Triangle, Area, Auxiliary Lines, iPad apps, Tutoring.

3 comments:

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

    ReplyDelete
  2. NOte that Triangles ABE and EHC are similar ( case AA)
    so AB/AE=FH/BC => AB.BC=AE.FH
    and area (ABCD)= area(FHJG)

    ReplyDelete
  3. AB=s, EB=a, EF=a', FH= s'
    EA=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

    ReplyDelete