SAT Mathematics Practice Test 5

Let w represent the width of the rectangular garden, in feet. Since the length of the garden will be $5$ feet longer than the width of the garden, the length of the garden will be $\mathit{w}+5$ feet. Thus the area of the garden will be $\mathit{w}\left(\mathit{w}+5\right)$.It is also given that the area of the garden will be 104 square feet. Therefore, $\mathit{w}\left(\mathit{w}+5\right)=104$, which is equivalent to ${\mathit{w}}^2+5\mathit{w}-104=0.$ The quadratic formula can be used or the equation above can be factored to result in $\left(\mathit{w}+13\right)\left(\mathit{w}-8\right)=0.$ Therefore, $\mathit{w}=8$ and $\mathit{w}=-13.$ Because width cannot be negative, the width of the garden must be 8 feet. This means the length of the garden must be $8+5=13$ feet.