Two sides of a rectangle are 3x+ 4y + 5 =0 and4x-3y + 15 = 0. If one of its vertices is (0, 0), then the area of the rectangle is _. 

 

$$\begin{gathered} Origin is not a point on any of the lines given \\ so that origin is a vertex which does not lies on the given sides \\ the perpendicular dis\tan ce from origin to one line is length of the rec\tan gle and the perpendicualr dis\tan ce from origin to the \\ second line is breadth of the rec\tan gle \end{gathered}$$Distance of (0, 0) from the given lines is 

$\begin{array}{l}a=\frac{|0+0+5|}{5}=1\\ b=\frac{|0-0+15|}{5}=3\\ \text{ Area of rectangle is }ab=3\text{ sq. units. }\end{array}$