Question 227710
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:
{{{120 = (x)(x-7)}}}
Now we solve this. Start by simplifying it (with the Distributive Property):
{{{120 = x^2 -7x}}}
Since this is a quadratic equation, get one side equal to zero (by subtracting 120 from each side):
{{{0 = x^2 -7x -120}}}
Now we can either factor this or use the quadratic formula:
{{{0 = (x - 15)(x+8)}}}
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:
{{{x-15 = 0}}} or {{{x+8 = 0}}}
Solving these we get:
{{{x = 15}}} or {{{x = -8}}}
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.