SOLUTION: I can get the equation and solve this but i am unsure how to apply it to get the dimensions of the rectangle. The problem is this: Find the dimensions of a rectangle whose width i

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Let x = length of the rectangle.
Since the width is 7 feet less, the width would be:
x - 7
Area of all rectangles is length * width (A = l*w). Substituting our expressions and the value for the ares of this rectangle we get:

Now we solve this. Start by simplifying it (with the Distributive Property):

Since this is a quadratic equation, get one side equal to zero (by subtracting 120 from each side):

Now we can either factor this or use the quadratic formula:

Now we use the Zero Product Property which tells us that this (or any) product can be zero only if one of the factors is zero. So:
or
Solving these we get:
or
Since x represents the length of the rectangle we must reject the negative answer. So the only possible length is 15. And the width, which is x-7, is 8.