Well this could be incredibly easy, by just saying 
and 
.
This is a completely valid case but nevertheless seems too easy. The requirements are probably that n and m are integers or natural numbers but since that was not specified such probable requirement ought not to be followed.
Hope this helps :)
Potential energy, though this seems like a question for the science section unless I'm missing something.
X(x+8)=(x+4)(x+3)
x^2+8x=x^2+7x+12
x=12
original length = 20
original width = 12
next length = 15
next width = 16
Angle: x
complement: 90-x
3x=90-x-14
4x=76
x = 19
90-x= 71
Answer: $9.00
.......................................
