Let S be the set of all triangles in the x y -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

Step-by-step solution

Since the vertex of given triangle is O (origin) and other two vertices A and B lies on the coordinate axes, hence triangle must be a right-angled triangle. Area = 1 2 x . y                                                 (   x ,   y ∈ I ) As per given condition 1 2 x . y = 50 ⇒ x .   y = 100 Possible ordered pairs of x ,   y when ∆ formed in 1 s t quadrant ar