Question 78740
The problem tells you that the Length (L) equals the Width (W) plus 3 feet. In equation 
form this becomes:
.
{{{L = W + 3}}}
.
The problem also tells you that the Area (A) is 54 square feet.  From geometry you know that
the formula for the Area of a rectangle is that Area equals the product of the Length
times the Width.  In equation form this is:
.
{{{A = L*W }}}
.
Substitute the given area to get:
.
{{{54 = L*W}}}
.
This equation has two unknowns. You can't solve it unless you can eliminate one of the
unknowns. To do that you can note that L = W + 3.  If you substitute W + 3 for L in the
equation you get:
.
{{{54 = (W + 3)*W}}}
.
And multiplying out the right side results in:
.
{{{54 = W^2 + 3W}}}
.
Get this into the standard quadratic form by first subtracting 54 from both sides and
then switching sides around to get:
.
{{{w^2 + 3W - 54 = 0}}}
.
This can be factored into:
.
{{{(W+9)*(W-6) = 0}}}
.
Notice that this equation will be true if either of the 2 factors is a zero because
zero times anything is zero and therefore equal to the right side of this equation.
.
Set W+9 equal to zero and solve to find that W = -9.  But what sense does a negative
width make in this case?  None at all, so disregard this solution.
.
Next set W-6 equal to zero and solve to find that W = +6. That's better. The width is
6 feet, and since we know that the length is 3 feet longer than the width, the length
has to be 9 feet.  Check by noting that the product of the length times the width is
9 ft times 6 ft and that equals the given area of 54 sq ft.
.
Hope this helps you to understand the problem a little better.