Your community wants to put a square fountain in a park. Around the fountain will be a sidewalk that is 3.5 ft wide. The total area that the fountain and sidewalk can be is 700 ft2. What are the dimensions of the fountain?
+130516 Let x be each side of the fountain....so we have
L x W = 700
(x + 7)(x + 7) = 700 simplify
x^2 + 14x + 49 = 700
x^2 + 14x - 651 = 0
Using the on-site solver, we have
$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{651}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
{\mathtt{x}} = {\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{33.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
{\mathtt{x}} = {\mathtt{19.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
\end{array} \right\}$$
So...each side of the fountain is about 19.46 ft
And the area is (19.46)^2 = 378.7 sq ft
+130516 Let x be each side of the fountain....so we have
L x W = 700
(x + 7)(x + 7) = 700 simplify
x^2 + 14x + 49 = 700
x^2 + 14x - 651 = 0
Using the on-site solver, we have
$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{651}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
{\mathtt{x}} = {\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{33.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
{\mathtt{x}} = {\mathtt{19.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
\end{array} \right\}$$
So...each side of the fountain is about 19.46 ft
And the area is (19.46)^2 = 378.7 sq ft
