Question

if perimeter of triangle is 12 how many triangles is possible to

Answer 1

Three.  Let the sides of the triangle be x, y and 12−(x+y).  Now, the sum of any two sides of a triangle is greater than its third side. So,  x+y>12−(x+y)  ∴x+y>6  Also, the difference of the two sides should be less than the third. So,  x−y<12−(x+y)  ∴x<6  Since x and y are arbitrary, y<6  Based on the above equations, x and y lies between 1 and 5. The acceptable unique pairs of x and y are:  (2, 5) (3, 4) (3, 5) (4, 4) (4, 5) (5, 5) While calculating the third side, we can see that pairs 1 and 6, and 2, 3 and 5, are the same. So we have 3 triangles:  (2, 5, 5) (3, 4, 5) (4, 4, 4)