9. How many different triangles with a perimeter of 15 cm can be constructed that have integral measurement of sides?

• Ans : 7
  1,7,7; 2,6,7; 3,6,6; 3,5,7; 4,5,6; 4,4,7; 5,5,5.
  There are 7 possible triangles.
• 11 years agoHelpfull: Yes(19) No(7)
• let the perimeter be p.
  no.of triangles if the odd numbered perimeter is given is p=2n-3.(where n is no.of triangles)
  no.of triangles if the even numbered perimeter is given is p=2n.
  given p=15cm.
  hence 15=2n-3
  n=9
  
• 11 years agoHelpfull: Yes(17) No(3)
• We have to find all choices of positive
  integers x, y, and z such that
  
  x + y + z = 15
  
  x + y + z = 15
  x + y > z
  x + z > y
  y + z > x
  
  From
  x + y + z = 15
  x + y = 15 - z
  
  and since x + y > z,
  15 - z > z
  15 > 2z
  7.5 > z
  
  From
  x + y + z = 15
  x + z = 15 - y
  
  and since x + z > y,
  15 - y > y
  15 > 2y
  7.5 > y
  
  From
  x + y + z = 15
  y + z = 15 - x
  
  and since y + z > x,
  15 - x > x
  15 > 2x
  7.5 > x
  
  So all the sides are 7 or less
  
  And since to make sure they are non-congruent,
  
  we'll require that x < y < z, so
  
  x = 1 y = 7 z = 7
  x = 2 y = 6 z = 7
  x = 3 y = 5 z = 7
  x = 3 y = 6 z = 6
  x = 4 y = 4 z = 7
  x = 4 y = 5 z = 6
  x = 5 y = 5 z = 5
  
  So there are 7.
  
• 11 years agoHelpfull: Yes(8) No(3)
• ans : 8
  177,267,366,357,456,447,555,573
• 11 years agoHelpfull: Yes(4) No(14)
• ans is 19
  (1,1,13)(1,2,12)(1,3,11)(1,4,10)(1,5,9)(1,6,8)(1,7,7)(2,2,11)(2,3,10)(2,4,9)(2,5,8)(2,6,7)(3,3,9)(3,4,8)(3,5,7)(3,6,6)(4,4,7)(4,5,6)(5,5,5)
• 11 years agoHelpfull: Yes(3) No(20)
• 14C2...AS Positive integral solution is given by (n-1)C(k-1)
  
• 11 years agoHelpfull: Yes(2) No(4)
• conditions are (1)a+b+c=15 & (2)summation of any two side > 3rd side
  so the combinations are: (1,7,7)(2,6,7)(3,5,7)&(4,4,7)
  therefore no of differnt triangles = 4
• 11 years agoHelpfull: Yes(2) No(4)
• Ans.7
  771,627,555,564,573,636,645
• 11 years agoHelpfull: Yes(1) No(1)
• soorryy...ans will be 7
• 11 years agoHelpfull: Yes(1) No(2)
• ans 9.
  (177),(267),(366),(357),(456),(447),(555),(573),(483).
  all possible triangles
• 11 years agoHelpfull: Yes(1) No(4)
• Sum of two sides should be greater than three sides. So, total number of triangles possible are 7
  1,7,7; 2,6,7; 3,6,6; 3,5,7; 4,5,6; 4,4,7; 5,5,5.
• 11 years agoHelpfull: Yes(1) No(0)
• perimeter of 15, the longest side must be 5, 6 or 7. If it is 5 then the middle side can be 5; if it is 6 then the middle side can be 5 or 6; if it is 7 then the middle side can be 4, 5, 6 or 7. Adding those up gives 1+2+4 = 7.
• 11 years agoHelpfull: Yes(0) No(3)