Mathematics - Point Question with Solution | TestHub

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$=\frac{1}{2}x.y ( x, y\in I)$

As per given condition

$\frac{1}{2}x.y=50\Rightarrow x. y=100$

Possible ordered pairs of$\left(x, y\right)$when$∆$formed in$1^{st}$quadrant are$9$i. e.$\left(1,100\right), \left(2,50\right), \left(4,25\right), \left(5,20\right), \left(10,10\right), \left(25, 4\right), \left(50, 2\right), \left(100,1\right)$

$∆$can be formed in any of the quadrants, hence total number of cases$9\times 4=36.$