Let the 3 sides of the triangle be 2n+1,2n+3,2n+5, where n≥0. So the triangles will be (1,3,5)for n=0 and (3,5,7)for n=1 and so on.
A condition the sides of a triangle should satisfy is the Triangle inequality. Sum of any two sides should be greater than the third side.
⇒2n+3+2n+5>2n+1
⇒2n+8>1
⇒2n>−7
∴n≥1
Since, the perimeter is less than 1000 units.
2n+1+2n+3+2n+5<1000
6n+9<1000
6n<991
n<165.17≈165
Hence, this is the answer.