the length of a rectangle exceeds its breadth by 4 cm. if length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm sqsq morthan that of the given rectangle. find the length and breadth of the given rectangle.
or - using one variable, as your title suggests
width --- x
length --- x+4
new width = x+3
new length = x+7
(x+3)(x+7) - x(x+4) = 81
x^2 + 10x + 21 - x^2 - 4x = 81
6x = 60
etc
If the width is x and the length y, then
y = x+4
(x+3)(y+3) = xy+81
Now just solve for x and y. If you expand the 2nd equation, you will see the xy drop out, leaving you with two linear equations in x and y.