Question

The area of a rectangle is 6x^2-xy -y^2 square units and its length os 3x + y units. findits breadth in terms of x and y.

Answer 1

The area of a rectangle is $6x^{2} -xy-y^{2}$ square units. 
The length of the rectangle is 3x+y units. 
∴ Breadth of rectangle = $\frac{6x^{2}-xy-y^{2} }{3x+y}$ units = $2x-y$ units

So, why did this happen? 
Well, if Length × Breadth = Area, then, Breadth = $\frac{Area}{Length}$. 
Similarly, Length = $\frac{Area}{Breadth}$. 

Hope this helps you.