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

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

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

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

$:\implies \sf Area = Length \times Breadth$

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

$:\implies \sf 360= {x}^{2} + 9x$

$:\implies \sf {x}^{2} + 9x - 360 = 0$

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

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

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

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

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

_____________________...

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

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

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