Answer
Length =$7$ ft
Width = $3$ ft
Work Step by Step
We know the following:
Length = $(x+4)$ ft
Width = $x$ ft
Area = $21$ $ft^2$
We also know that the formula for the area of a rectangle is Length $\times$ Width.
We can substitute the values mentioned earlier into this formula to form a quadratic equation!
Area = Length $\times$ Width.
$21 = (x+4) \times x$
$21 = x^2+4x$ (Subtract 21 from both sides to make the equation = 0)
$x^2+4x-21=0$
We can then solve this equation by factoring;
$x^2+7x-3x-21=0$
$x(x+7)-3(x+7)=0$
$(x-3)(x+7)=0$
We can make both brackets=0 to find a solution for $x$.
$(x-3)=0$, or $(x+7)=0$
$x=3$ or $x=-7$
We only want 1 solution however in this case, and it cannot be a negative number as we are trying to find the width of a rectangle, which cannot be below 0. So, $x=3$.
Length = $(3)+4$
= $7$ ft
Width = $3$ ft
