The number of isosceles triangles with integer sides if no side exeeds 2016 is

Options

A. `(1008)^(2)` if equal sides do not exceed `1008`
B. `2(1008)^(2)` if equal sides exceed `1008`
C. `3(1008)^(2)` if equal side have any length exceeding 2016
D. `(2016)^(2)` if equal sides have any length not exceeding 2016

Answer

A, B, C, D

Explanation

If equal side have length `n`, then the number of triangles will be `2n-1`.
So if equal side does not exceed `1008,` no. of triangles `=1+3+5+…1008` terms `=(1008)^(2)`
if equal side does exceed `1008`. No of triangles `=2016+2016+2016+…1008` terms `=2(1008)^(2)`