[tex]\huge\underline{\frak{ \: \: \: \: \: \: Solution : \: \: \: \: \: \: }} \\ \\ [/tex]
[tex]\frak {\pink{Let}}\begin{cases} \sf{\red{Breadth \: be \: x}}\\ \sf{\orange{The \: Length = x + 9}}\end{cases} \\ [/tex]
[tex]\bigstar \: \underline{\textsf{According to the given Question :} }\\ \\[/tex]
[tex]:\implies \sf Area = Length \times Breadth \\ \\ \\ [/tex]
[tex]:\implies \sf 360=(x + 9 ) x \\ \\ \\ [/tex]
[tex]:\implies \sf 360= {x}^{2} + 9x \\ \\ \\ [/tex]
[tex]:\implies \sf {x}^{2} + 9x - 360 = 0\\ \\ \\ [/tex]
[tex]:\implies \sf {x}^{2} + 24x - 15x - 360 = 0\\ \\ \\ [/tex]
[tex]:\implies \sf x(x + 24) - 15(x + 24) = 0\\ \\ \\ [/tex]
[tex]:\implies \sf (x + 24) \: (x - 15) = 0\\ \\ \\ [/tex]
[tex]:\implies \underline{ \boxed{ \sf x = - 24 \: or \: x = 15}}\\ \\ \\ [/tex]
[tex]\therefore\:\underline{\textsf{Ignoring the negative value, the Breadth of rectangular garden is \textbf{15 ft}}}. \\ \\ \\ [/tex]
[tex]\bigstar \: \underline{\textsf{Dimensions of rectangular garden :}} \\ \\ [/tex]
[tex]\bullet\:\:\textsf{The Breadth of rectangular garden = x = \textbf{15 ft.}} \\ \\ [/tex]
[tex]\bullet\:\:\textsf{The Length of rectangular garden = x + 9 = 15 + 9 = \textbf{24 ft.}} \\ \\ [/tex]
