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

Answer:

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

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

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

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

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

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

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

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

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

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

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

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

_____________________...

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

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

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

Answer 2

Question:-

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

$\huge{\underline{\mathtt{\red{ƛ}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}} \red♡$

The area A = 360 square ft.

And the one condition “ 9 ft. longer than it is width.”

Find out, both the dimensions of the rectangular garden = ?

The value of the length L = W + 9

Area A = { Length × width }

360 = { (W + 9) × W }

W ^ 2 + 9W -360 = 0

Now it is a quadratic equations it has two roots.

W ^ 2 + (24–15)W -360=0

W ^ 2 + 24W -15W -360=0

W(W +24)-15(W+24)=0

(W+24)(W-15)=0

There are two value of we get,

(W +24)=0, W = -24 ( not valid value )

If W -15=0, W=15 ft. answer (dimension)

The value of length L = W + 9 = 15+9= 24 ft.

L= 24 ft. answer ( dimension)

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