Q. How many such rectangles are possible with its area equals to its perimeter ?

Options
1) Only 1
2) Only 2
3) Only 3
4) None of the above.

• more than 3
  lb=2(l+b) solve u'll get l=2b/(b-2)
  sub the values 3,4,6 etc ..
  more than 3 ..
• 11 years agoHelpfull: Yes(22) No(4)
• 4th option was more than 3 ...
  vales will be (3,6),(6,3),(4,4) ...
• 11 years agoHelpfull: Yes(5) No(2)
• Actually,
  for rectangle always
  lb>2(l+b)
  so,
  it will be..
  4a=a*a;
  a=4;
  Hence, only 1
  4a=a*a
• 11 years agoHelpfull: Yes(3) No(14)
• l=2b/(b-2)
  possible integer pairs(6,3),(3,6),(4,4)
  (6,3) and (3,6) represent same figure and (4,4) is a square
  only one possible integer pAIR
  if x,y are not integers then many pairs are possible
• 11 years agoHelpfull: Yes(3) No(1)
• all squares are rectangles becoz for rectangle condition is opposite sides are equal.
  so there is possibility of having more than 3 ,option 4 is ans
• 11 years agoHelpfull: Yes(2) No(0)
• i think (3,6) and (6,3) will be considered as same..
• 10 years agoHelpfull: Yes(2) No(0)
• lb=2(l+b)
  l=2b/b-2
  put values of b..clearly b>2...
  put b=3,l=6
  put b=4 l-4
  put b=5 l=nt psbl.. n so on.
  so no of rectangles can be >3
  option 4 is correct..
  
• 11 years agoHelpfull: Yes(1) No(1)
• more than 3 ..
• 10 years agoHelpfull: Yes(0) No(0)
• If length and breadth should be integer then only 2 rectangles are possible of L,B=(3,6) and (6,3)... And if there is no such condition,more than 3 rectangles are possible
• 10 years agoHelpfull: Yes(0) No(0)
• https://nrich.maths.org/6398/solution
  
  There are an infinite number of these rectangles.
• 7 years agoHelpfull: Yes(0) No(0)