How many distinct rectangles having integral sides and a perimeter less than equal to 150 cm are possible

• L can have values 1 ,2,3..........38
  B can have values 1.,2,3,4.......37
  
  so total 38*37=1406
• 13 years agoHelpfull: Yes(2) No(2)
• L+BB otherwise rectangle with dimensions 37x36 and 36x37 are same. here we are interested in distinct rectangles.
  For L=35, 35 rectangles are possible.
  ..
  ..
  For L=1, only one rectangle 1x1 is possible.
  
  so total rectangles will be
  
  2*(1+2+...37)= 2*37*38/2 = 1406 .. same as given by Dipin.
• 13 years agoHelpfull: Yes(2) No(0)
• 
  L+BB so rectangle with L=37 and B=38 is not considered
  otherwise rectangle with dimensions 37x38 and 38x37 are same. here we are interested in distinct rectangles.
  For L=36, 36 rectangles are possible.
  For L=35, 35 rectangles are possible.
  ..
  ..
  For L=1, only one rectangle 1x1 is possible.
  
  so total rectangles will be
  
  2*(1+2+...37)= 2*37*38/2 = 1406 .. same as given by Dipin.
• 13 years agoHelpfull: Yes(1) No(0)
• If length = 1 then breadth = 1
  if length = 2 then breadth = 1,2
  similarly for length = 37, breadth = 1,2,3,4........,37
  after that for length = 38, breadth = 1,2,3,4.......,37
  for length = 39, breadth = 1,2,3,4,5......36
  and for length = 74, breadth = 1
  so total possibilities = 1+2+3+4+........+37+37+36+35+.........+2+1 = 2*37*38/2
  = 37*38 = 1406
• 13 years agoHelpfull: Yes(1) No(0)
• If L is length and B is breadth, then
  as per condition
  L+ B
• 13 years agoHelpfull: Yes(0) No(1)
• 38*37 = 1406
  
  If L is length and B is breadth, then
  as per condition
  L+ B
• 13 years agoHelpfull: Yes(0) No(0)
• f length=1 then (1,1) (1,2) (1,3) ......(1,74)==74ractangles
  if length=2 then (2,1) (2,2) (2,3) ......(2,73)==73 ractangles
  similarly 72,71,70....upto1
  now if i m doing mistak then please mention it your reply
  it should be 2755 ractangles
• 13 years agoHelpfull: Yes(0) No(1)
• Answer not getting posted completely.
  L+B
• 13 years agoHelpfull: Yes(0) No(0)
• thanks to dipin and dimple. i was confuced that should i treat (1,2) and (2,1) dimention ractangles as different or as same bt acording to u it should be same.........
• 13 years agoHelpfull: Yes(0) No(0)
• if one side of rectangle is 1 ... other side can be between 1 and 73 ... total no. of possibilities = 73
  
  if one side is 2 .. other side can be anything between 2 and 72 ... total no. of possibilities = 71
  
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  similalry it will go till combination of 37 and 37 where total possibilities = 1
  
  thus total no of rectangles that can be formed are 1+3+5+.....+73 (Sum of odd nos.)
  
  using geometric progression the sum comes out to be 1369 ...........ANS
  
• 13 years agoHelpfull: Yes(0) No(0)