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

Question

3 years ago

15

ns of the garden in feet

1 answer:

rosijanka [135] · Answer 1 · 2022-03-28T18:53:25+03:00

6 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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