Question 155170

Let x = length


The area of a rectangle is 28 sq ft and the width is 3 feet shorter than the length



So the width is the expression: {{{x-3}}}



So the area is 



Area = length * width



{{{A = x(x-3)}}} Plug in the length of “x” and the width of {{{x-3}}}



{{{28 = x(x-3)}}} Plug in {{{A=28}}}



{{{28 = x^2-3x}}} Distribute



{{{0=x^2-3x-28}}} Subtract 28 from both sides.



{{{0=(x+4)(x-7)}}} Factor the right side.



{{{(x+4)(x-7)=0}}} Rearrange the equation.



So the solutions are {{{x=-4}}} and {{{x = 7}}} which means that the width is 7 units.