Mathematics - Permutation & Combination Question with Solution | TestHub

If the sides are $\mathrm{a},\mathrm{a},\mathrm{b}$ then the triangle forms only when $2a>b$. So for any $a\in N,\mathrm{b}$ can change from 1 to $2a-1$. When $a\le 1004$ then number of triangles $=1+3+5+..+(2(1004)-1)=(1004{)}^2$ and if $1005\le a\le 2008$, b can take any value from 1 to 2008, but a has 1004 possibilities; hence number of triangles $=1004\times 2008=2(1004{)}^2$ ∴ Total number of isosceles triangles $=3(1004{)}^2$