One of the possible ∆OAB is A(a,0) and B(0,b). Area of ∆OAB=
1
2
|ab| ∴|ab|=100 |a||b|=100 But 100=1×100,2×50,4×25,5×20 or 10×10 ∴ For 1×100,a=1 or -1 and b=100 or -100 ∴ Total possible pairs are 8 Total possible pairs for 1×100,2×50,4×25 or 5×20 are 4×8 And for 10×10 total possible pairs are 4 ∴ Total number of possible triangles with integral coordinates are 4×8+4=36