A square ABCD shares 25% of its area with a rectangle AEFG, such that AE>AB and A, B, E are collinear. Also, rectangle AEFG shares 50% of its area with the square ABCD. Find AE/AG.

• draw diagram,
  
  let side of square =4x
  length of rectangle = 2*4x = 8x [as,rectangle AEFG shares 50% of its area with the square ABCD]
  breadth of rectangle= 4x/4 = x [as,square ABCD shares 25% of its area with rectangle AEFG]
  
  so, AE=8x, AG=x => AE/AG = 8x/x = 8
  
• 10 years agoHelpfull: Yes(30) No(0)
• Let’s assume side of square is x
  and side of rectangle is y
  We know that A, B & E are Collinear , so our square & rectangle position with we like this
  A-------------B------------E
  | | |
  G--------------------------F
  | |
  | |
  | |
  D-------------C
  Let’s assume side of square is x=AB=BC=DC=AD
  and other side of rectangle is y=AG=EF
  
  According to condition, if A, B & E are in same line and rectangle share 50 % of its area with square than means
  Rectangle ABOG=BEFO and from it we can make that AB=BE=x as we assumed.
  
  Square area = x^2
  Rectangle area = (2*x)*y…(because AE=2*x)
  Cond 1) 25 % area of square shared with rectangle,
  Cond2) 50% area of rectangle shared with square,
  So by these condition we can conclude that 25% of square area equals with 50% of rectangle’s area,
  Putting these we get, (x^2)/4={(2*x)*y}/2
  =>x=4*y………………(i)
  
  Need to FIND : AE/AG => (2*x)/y
  Put eq (i) into this, (2*4*y)/y=8
  Answer = 8 units
  
• 10 years agoHelpfull: Yes(11) No(0)
• ans is 8:1.
  
• 10 years agoHelpfull: Yes(0) No(0)