Okay so you start with what you know. Hopefully you know that the formula for the area of a rectangle is:
A = L * W
where A is area, L is length, and W is width. You know A = 45m^2. Also, you know that (W + 4m) is equal to the length, L. So, rewriting your equation with the given values, you get:
45m^2 = (W + 4)*W
Now, all you have to do is solve for W. You can do this two ways with a calculator of some sort that solves for variables (e.g. a graphing calculator), or by using the quadratic formula:
Ax^2 + Bx + C = 0
[-B +or- sqrt(B^2 - (4*A*C))] / (2*A) = x
First you have to get our Area formula into the Ax^2 + Bx + C format (I'm dropping the units, m, for clarity's sake) :
45 = (W + 4)*W
0 = (W + 4)*W - 45
0 = W^2 + 4*W - 45
so now,
A = 1
B = 4
C = -45
plug these values into the quadratic formula
[-(4) +or- sqrt((4)^2 - (4*(1)*(-45)))] / (2*(1)) = W
you get two solutions for W (because of the +or- part of the quadratic formula) :
5m and -9m
http://tinyurl.com/yo6jpk
Obviously, the width cannot be a negative number, right? So, 5m must be the width. Therefore the length (W + 4) is 9m. Plug these values back into the area formula to make sure they work:
A = 5m * 9m = 45m^2
( m*m = m^2 )
It does work! Hope this helps somewhat. When looking at the quadratic formula remember that I switched x with W to fit our problem. Also A and B are just the coefficients of X^2, X, and the constant is C.