Respuesta :
Given:
The area of the pond, A=63 m^2.
Let l be the length and w be the width of the rectangular pond.
It is given that the pond has length 2m more than twice it's width.
Hence, the expression for the length of the pond is,
[tex]l=2+2w\text{ ---(1)}[/tex]Now, the area of the rectangular pond can be expressed as,
[tex]\begin{gathered} A=lw \\ =(2+2w)w \\ =2w+2w^2 \end{gathered}[/tex]Since A=63, we get
[tex]\begin{gathered} 63=2w+2w^2\text{ } \\ 2w^2+2w-63=0\text{ ---(2)} \end{gathered}[/tex]The above equation is in the form of a quadratic equation given by,
[tex]ax^2+bx+c=0\text{ ---(3)}[/tex]Comparing equations (2) and (3), we get a=2, b=2, c=-63 and x=w.
Solve equation (2) for w using discriminant method.
[tex]\begin{gathered} w=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a} \\ =\frac{-2\pm\sqrt[]{2^2-4\times2\times(-63)}}{2\times2} \\ =\frac{-2\pm2\sqrt[]{127}}{4} \end{gathered}[/tex]Since width w cannot be negative ,
[tex]\begin{gathered} w=\frac{-2+2\sqrt[]{127}}{4} \\ =5.13 \end{gathered}[/tex]Put w=5.13 in equation (1).
[tex]\begin{gathered} l=2+2\times5.13 \\ l=12.26 \end{gathered}[/tex]Therefore, the length of pond is approximately 12.26 m and its width is approximately 5.13 m.
