Q. The angles of 2 sides of quadrilateral B and D are 90 degree each. BP and DQ are perpendicular to diagonal AC and it trisects the AC(AP=PQ=QC). Side AB is 4cm then find perimeter of quadrilateral.

• B,D are 90 so its a rectangle
  let AD=X then AC^2=(16+X^2) AP=AC/3
  SO AP^2=AC^2/9=(16+X^2)/9
  BP^2=AB^2-AP^2=16-{(16+X^2)/9}
  equate area of triangle ABC
  (1/2)*AC*BP = (1/2)*AB*BC
  or AC^2*BP^2 = AB^2*BC^2
  or (16+x^2)*[16-{(16+X^2)/9}]=16*x^2
  after solving
  x^4+32x^2-32*64=0
  x^2= 32 or -64
  x^2=32
  so x=4*(sqrt 2)
  perimeter of quadrilateral=2(x+4)
  =2[4*(sqrt 2)+4]
  =8(1+sqrt(2))
• 11 years agoHelpfull: Yes(16) No(8)
• https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-frc3/1476375_268402199980030_2069894024_n.jpg THIS IS THE IMAGE OF DIAGRAM ..
  
• 10 years agoHelpfull: Yes(8) No(2)
• Rakesh could you please provide the diagram....please
• 11 years agoHelpfull: Yes(4) No(0)
• 
  ______________ _
  A| / |D
  | p / |
  | / Q/ |
  B|/___________ __|C
  
  BP_|_AC
  DQ_|_AC
  AB_|_BC
  DC_|_AD
  so right angle traingles are ABC,DAC,ABP,DQC,BPC,ADQ...but we just need 3 of them
  take ABC, ABP & BPC
  
  AB=DC=4;
  Let AD=BC=x;
  Let AP=a;
  so AC=3a;
  
  from |_ ABC
  x^2-16=9a^2; ---------(1)
  
  
  from |_ ABP
  BP^2=16-a^2 ---------(2)
  
  
  from |_ BPC
  
  16-a^2=x^2-4a^2 (use 2)
  3a^2=x^2-16 ---------(3)
  
  from (1) & (3)
  x^2-16=3x^2-48
  32=2x^2
  
  x=4(2)^1/2
  
  so perimeter=8+8(2)^1/2
  
  
  
• 10 years agoHelpfull: Yes(2) No(0)
• first,it may or may not be rectangle.
  second,let us consider x to be 3 equally divided line segments.
  so perimeter would be equal to 4*square root of (9x^2-y^2).
  
• 11 years agoHelpfull: Yes(1) No(4)
• 9 1's are there.dont confuse here
  first multiply the numbers where ever multiplication symbol is present then go for repective binary format.then count number of 1's.u ll get it.
  
• 11 years agoHelpfull: Yes(0) No(1)
• nt gettng d soln..could sm1 explain please..
• 11 years agoHelpfull: Yes(0) No(1)
• 18 be the perimeter
  
• 11 years agoHelpfull: Yes(0) No(1)