is perimeter of triangle > 30? a,b,c are sides of triangle.
a. a-b=15;
b. area of triangle 15.

• Statement 1: a-b = 15.
  The third side of a triangle must be greater than the difference between the lengths of the other 2 sides.
  Thus:
  c > a-b
  c > 15.
  
  Since a-b = 15, a = b+15.
  Thus:
  Perimeter = a + b + c = (b+15) + b + (more than 15) = 2b + (more than 30).
  SUFFICIENT.
  
  Statement 2: area = 50
  Given a triangle with perimeter p, the maximum possible area will be yielded if the triangle is EQUILATERAL.
  Thus, if p=30, then the maximum possible area will be yielded if each side = 10.
  The area of an equilateral triangle = (s²√3)/4.
  If p=30 and s=10, then the area = (10²√3)/4 = 25√3 = less than 50.
  Implication:
  The maximum possible area of a triangle with a perimeter of 30 is LESS THAN 50.
  Since statement 2 requires that the area be EQUAL TO 50, the perimeter of the triangle must be GREATER THAN 30.
  SUFFICIENT.
• 6 years agoHelpfull: Yes(10) No(1)
• sum of any two sides is greater than the third side
  say a+b+c=30
  given a-b=15
  a=15+b
  15+2b+c=30
  c must be greater than 15 and hence the permitre also must be greater than 15
• 4 years agoHelpfull: Yes(0) No(0)