Question

A rectangular garden has an area of 360 square feet. the length of the garden is 9 feet longer than the width. find the dimensions of the garden in feet

Answer 1

`\huge\underline{\frak{ \: \: \: \: \: \: Solution : \: \: \: \: \: \: }} \\ \\`

`\frak {\pink{Let}}\begin{cases} \sf{\red{Breadth \: be \: x}}\\ \sf{\orange{The \: Length = x + 9}}\end{cases} \\`

`\bigstar \: \underline{\textsf{According to the given Question :} }\\ \\`

`:\implies \sf Area = Length * Breadth \\ \\ \\`

`:\implies \sf 360=(x + 9 ) x \\ \\ \\`

`:\implies \sf 360= {x}^(2) + 9x \\ \\ \\`

`:\implies \sf {x}^(2) + 9x - 360 = 0\\ \\ \\`

`:\implies \sf {x}^(2) + 24x - 15x - 360 = 0\\ \\ \\`

`:\implies \sf x(x + 24) - 15(x + 24) = 0\\ \\ \\`

`:\implies \sf (x + 24) \: (x - 15) = 0\\ \\ \\`

`:\implies \underline{ \boxed{ \sf x = - 24 \: or \: x = 15}}\\ \\ \\`

`\therefore\:\underline{\textsf{Ignoring the negative value, the Breadth of rectangular garden is \textbf{15 ft}}}. \\ \\ \\`

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`\bigstar \: \underline{\textsf{Dimensions of rectangular garden :}} \\ \\`

`\bullet\:\:\textsf{The Breadth of rectangular garden = x = \textbf{15 ft.}} \\ \\`

`\bullet\:\:\textsf{The Length of rectangular garden = x + 9 = 15 + 9 = \textbf{24 ft.}} \\ \\`