The area of a rectangular plot is 582 m the length of the plot is one

1.	The area of a rectangular plot is 582 m the length of the plot is one more than twice its breadth find the length and breadth of the plot
Answer» $\blue{\bold{\underline{\underline{Answer:}}}}$ $\green{\tt{\therefore{Length=34.6\:m}}}$ $\green{\tt{\therefore{Breadth=16.8\:m}}}$ $\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$ $\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt: \implies Area \: of \: rectangle = 582 \: {m}^{2} \\ \\ \tt: \implies Length \: of \: plot \: is \: one \: more \: that \: twice \: its \: Breadth \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length = ? \\ \\ \tt: \implies Breadth = ?$ • ACCORDING to given QUESTION : $\circ \: \text{Let \: Breadth \: be \: x} \\ \\ \circ \: \text{Length = 1 + 2x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: rectangle = Length \times Breadth \\ \\ \tt: \implies 582 = (1 + 2x) \times x \\ \\ \tt: \implies 582 = x + 2 {x}^{2} \\ \\ \tt: \implies {2x}^{2} + x - 582 = 0 \\ \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{ {1}^{2} - 4 \times 2 \times 582 } }{2 \times 2} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{1 + 4656} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{4657} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm68.2}{4} \\ \\ \tt: \implies x = \frac{67.2}{4} \\ \\ \green{\tt: \implies x = 16.8 \: m} \\ \\ \bold{Note-} \: \tt{ Length \: and \:Breadth \: cannot \: be \: in \: negative} \\ \\ \green{\tt \therefore Length = 1 + 2 \times 16.8 = 34.6 \: m} \\ \\ \green{\tt \therefore Breadth = x = 16.8 \: m}$

The area of a rectangular plot is 582 m the length of the plot is one more than twice its breadth find the length and breadth of the plot

Answer»

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Length=34.6\:m}}}$

$\green{\tt{\therefore{Breadth=16.8\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt: \implies Area \: of \: rectangle = 582 \: {m}^{2} \\ \\ \tt: \implies Length \: of \: plot \: is \: one \: more \: that \: twice \: its \: Breadth \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length = ? \\ \\ \tt: \implies Breadth = ?$

• ACCORDING to given QUESTION :

$\circ \: \text{Let \: Breadth \: be \: x} \\ \\ \circ \: \text{Length = 1 + 2x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: rectangle = Length \times Breadth \\ \\ \tt: \implies 582 = (1 + 2x) \times x \\ \\ \tt: \implies 582 = x + 2 {x}^{2} \\ \\ \tt: \implies {2x}^{2} + x - 582 = 0 \\ \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{ {1}^{2} - 4 \times 2 \times 582 } }{2 \times 2} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{1 + 4656} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{4657} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm68.2}{4} \\ \\ \tt: \implies x = \frac{67.2}{4} \\ \\ \green{\tt: \implies x = 16.8 \: m} \\ \\ \bold{Note-} \: \tt{ Length \: and \:Breadth \: cannot \: be \: in \: negative} \\ \\ \green{\tt \therefore Length = 1 + 2 \times 16.8 = 34.6 \: m} \\ \\ \green{\tt \therefore Breadth = x = 16.8 \: m}$

The area of a rectangular plot is 582 m the length of the plot is one more than twice its breadth find the length and breadth of the plot

• ACCORDING to given QUESTION :

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