Respuesta :
First we find the area of the first park
[tex]\begin{gathered} A=w\times l \\ A=60\times105 \\ A=6300 \end{gathered}[/tex]area is 6300 square meters
now find the perimeter
[tex]\begin{gathered} P=2w+2l \\ P=2(60)+2(105) \\ P=330 \end{gathered}[/tex]perimeter is 330 meters
now we need to write equations to find the measures of the another park and we can write from the statements
has the same perimeter
[tex]2w+2l=330[/tex]but a smaller area
then we choose an area smaller than 6300, for example 6000
[tex]w\times l=6000[/tex]now we have two equations and two unknows
[tex]\begin{gathered} 2w+2l=330 \\ w\times l=6000 \end{gathered}[/tex]then we can solve a unknow from one equation and replace on the other
I will solve w from the first equation and replace on second
[tex]\begin{gathered} 2w=330-2l \\ w=\frac{330-2l}{2} \\ \\ w=165-l \end{gathered}[/tex][tex]\begin{gathered} w\times l=6000 \\ (165-l)\times l=6000 \\ 165l-l^2=6000 \end{gathered}[/tex]rewrite the equation
[tex]l^2-165l+6000=0[/tex]and use quadratic formula to solve L
[tex]\begin{gathered} l=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ l=\frac{-(-165)\pm\sqrt[]{(-165)^2-4(1)(6000)}}{2(1)} \\ \\ l=\frac{165\pm\sqrt[]{27225-24000}}{2} \\ \\ l=\frac{165\pm\sqrt[]{3225}}{2} \end{gathered}[/tex]then we have two values for l
[tex]\begin{gathered} l_1=\frac{165+\sqrt[]{3225}}{2}=110.9 \\ \\ l_2=\frac{165-\sqrt[]{3225}}{2}=54.1 \end{gathered}[/tex]we can take any value because both are positive and replace on any equation to find w
I will replace l=110.9 to find w
[tex]\begin{gathered} w\times l=6000 \\ w\times110.9=6000 \\ w=\frac{6000}{110.9} \\ \\ w=54.1 \end{gathered}[/tex]Finally the length and wifth of the other rectangle patks are
[tex]\begin{gathered} l=110.9 \\ w=54.1 \end{gathered}[/tex]meters
