The length of the sides of a triangle are in integers and its area
>is also an integer. One side is 21 cm and the perimeter is 48 cm,
>then the length of the shortest side is :

• ans:84
  
  Sum of other 2 sides = 27.
  => If one side = x, other = 27 - x.
  Using Heron's formula,
  => A^2 = 24*3*(24-x)*(x-3)
  RHS must be a perfect square
  => A^2 = 6^2 * 2 * (24-x)(x-3) is a perfect square
  => x = 10, Other side = 17
  => shortest side = 10 cm.
  Other sides are 17 and 21 cm,
  Area = 84 sq cm.
• 13 years agoHelpfull: Yes(11) No(4)
• shortest side is 10 cms.
  
  all 3 sides are 10,17,21 cms.
• 13 years agoHelpfull: Yes(3) No(2)
• The length of the sides of a triangle are in integers and its area
  >is also an integer. One side is 21 cm and the perimeter is 48 cm,
  >then the length of the shortest side is :
  Read more at http://www.m4maths.com/3598-The-length-of-the-sides-of-a-triangle-are-in-integers-and-its-area-is-also-an-integer-One-side.html#OXJQs7r9Ml1C1KKA.99
• 9 years agoHelpfull: Yes(0) No(0)
• The length of the sides of a triangle are in integers and its area
  >is also an integer. One side is 21 cm and the perimeter is 48 cm,
  >then the length of the shortest side is :
  Read more at http://www.m4maths.com/3598-The-length-of-the-sides-of-a-triangle-are-in-integers-and-its-area-is-also-an-integer-One-side.html#oVaQlqv3VGR9vOEG.99
• 9 years agoHelpfull: Yes(0) No(0)