Question

the area of a rectangular plot is 582m².the length of the plot (in metres)is more than twice its breadth . find the length and breadth of the plot.​

Answer 1

Proper Question :

• The area of a rectangular plot is 582m² & the length of the plot (in metres) is one more than twice its breadth . Find the length and breadth of the plot.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Given that , The length of a rectangular plot is one more than twice it's breadth & Area of the rectangular plot is 582 m² .

Exigency To Find : The Length and Breadth of Rectangular plot ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that Breadth of Rectangular plot  x m and Length of Rectangular plot is  ( 2x + 1 )  m , i.e. length of a rectangular plot is one more than twice it's breadth.

As , We know that ,

• Formula for Area of Rectangle :

$\qquad \dag\:\:\bigg\lgroup \pmb{\bf Perimeter _{(Rectangle)} \:: l \:\:\times \:b \:\:\:\:sq.units \:}\bigg\rgroup$

⠀⠀⠀⠀⠀Here , l is the Length of Rectangle , b is the Breadth of Rectangle & Area of Rectangle is 582 m² .

$\qquad \dashrightarrow \sf Area _{(Rectangle)} \:=\: l \:\times \:b\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf Area _{(Rectangle)} \:=\: l \:\times \:b\:\\\\\qquad \dashrightarrow \sf 582 \:=\: \Big\{ ( 2x + 1 ) \times  x \Big\} \:\\\\\qquad \dashrightarrow \sf 582 \:=\: \Big\{ ( 2x + 1 ) \times x \Big\} \:\\\\ \qquad \dashrightarrow \sf 582 \:=\: \Big\{ 2x^2 + x \Big\} \:\\\\ \qquad \dashrightarrow \sf 2x^2 + x - 582 \:=\:0 \:\\\\ \qquad \dashrightarrow \sf 2x^2 + 33x - 32x - 582 \:=\:0 \:\\\\ \qquad \dashrightarrow \sf x( 2x + 33 ) - 16 ( 2x + 33 ) \:=\:0 \:\\\\\qquad \dashrightarrow \sf x( 2x + 33 ) - 16 ( 2x + 33 ) \:=\:0 \:\\\\\qquad \dashrightarrow \sf ( x - 16 ) ( 2x + 33 ) \:=\:0 \:\\\\ \qquad \dashrightarrow \sf x \:=\:16 \:\:or \:\: - \dfrac{33}{2} \:$

⠀━━ Dimensions cannot be in negative " -ve " .

$\qquad \dashrightarrow \sf x \:=\:16 \:\:or \:\: - \dfrac{33}{2} \:\\\\ \qquad \dashrightarrow \underline {\boxed{\pmb{\frak{\purple { x \:=\:16 \:m }}}}}\:$

Therefore,

• Length of Rectangular plot is ( 2x + 1 ) = 2(16) + 1 = 33 m
• Breadth of Rectangular plot is x = 16 m

$\qquad \therefore \underline {\sf \:Hence, \:The \:Length \:and \:Breadth \:of \:Rectangle \: is \: \pmb{\bf 16 \: m \:\& \: 33 \:m \:}\:, respectively. \:}$

━━━━━━━━━━━━━━━━━━

$\qquad \qquad \underline {\bigstar\;\:\pmb{\mathbb{ MORE \:\:FORMULAS\::\:}}}\:$

$\:\:\sf (I)\:\: Area \:of \:Triangle \:\:\::\:\bf{ Area_{(\triangle)} \:=\:\dfrac{1}{2} \times b \:\times h } \:\\\\\:\:\sf (II)\:\: Area \:of \:Parallelogram \:\:\::\:\bf{ Area_{(Parallelogram)} \:=\: b \:\times h } \:\\\\\:\:\sf (III)\:\: Area \:of \:Square \:\:\::\:\bf{ Area_{(\square)} \:=\: Side \:\times Side } \:\\\\\:\:\sf (IV)\:\: Area \:of \:Trapezium \:\:\::\:\bf{ Area_{(Trapezium)} \:=\: \dfrac{1}{2} \:\times h \: \:\times ( a + b ) } \:$

Answer 2

Proper Question :

• The area of a rectangular plot is 582m² & the length of the plot (in metres) is one more than twice its breadth . Find the length and breadth of the plot.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Given that , The length of a rectangular plot is one more than twice it's breadth & Area of the rectangular plot is 582 m² .

Exigency To Find : The Length and Breadth of Rectangular plot ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that Breadth of Rectangular plot x m and Length of Rectangular plot is ( 2x + 1 ) m , i.e. length of a rectangular plot is one more than twice it's breadth.

⠀⠀⠀

As , We know that ,

Formula for Area of Rectangle :

$\begin{gathered}\qquad \dag\:\:\bigg\lgroup \pmb{\bf Perimeter _{(Rectangle)} \:: l \:\:\times \:b \:\:\:\:sq.units \:}\bigg\rgroup \\\\\end{gathered}$

⠀⠀⠀⠀⠀Here , l is the Length of Rectangle , b is the Breadth of Rectangle & Area of Rectangle is 582 m² .

$\begin{gathered}\qquad \dashrightarrow \sf Area _{(Rectangle)} \:=\: l \:\times \:b\:\\\\\end{gathered}$

⠀⠀⠀⠀⠀⠀$\begin{gathered}\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\\end{gathered}$

$\begin{gathered}\qquad \dashrightarrow \sf Area _{(Rectangle)} \:=\: l \:\times \:b\:\\\\\qquad \dashrightarrow \sf 582 \:=\: \Big\{ ( 2x + 1 ) \times x \Big\} \:\\\\\qquad \dashrightarrow \sf 582 \:=\: \Big\{ ( 2x + 1 ) \times x \Big\} \:\\\\ \qquad \dashrightarrow \sf 582 \:=\: \Big\{ 2x^2 + x \Big\} \:\\\\ \qquad \dashrightarrow \sf 2x^2 + x - 582 \:=\:0 \:\\\\ \qquad \dashrightarrow \sf 2x^2 + 33x - 32x - 582 \:=\:0 \:\\\\ \qquad \dashrightarrow \sf x( 2x + 33 ) - 16 ( 2x + 33 ) \:=\:0 \:\\\\\qquad \dashrightarrow \sf x( 2x + 33 ) - 16 ( 2x + 33 ) \:=\:0 \:\\\\\qquad \dashrightarrow \sf ( x - 16 ) ( 2x + 33 ) \:=\:0 \:\\\\ \qquad \dashrightarrow \sf x \:=\:16 \:\:or \:\: - \dfrac{33}{2} \:\\\\\end{gathered}$

⠀━━ Dimensions cannot be in negative " -ve " .

$\begin{gathered}\qquad \dashrightarrow \sf x \:=\:16 \:\:or \:\: - \dfrac{33}{2} \:\\\\ \qquad \dashrightarrow \underline {\boxed{\pmb{\frak{\purple { x \:=\:16 \:m }}}}}\:\\\\\end{gathered}$

Therefore,

• Length of Rectangular plot is ( 2x + 1 ) = 2(16) + 1 = 33 m
• Breadth of Rectangular plot is x = 16 m

⠀⠀⠀

$\begin{gathered}\qquad \therefore \underline {\sf \:Hence, \:The \:Length \:and \:Breadth \:of \:Rectangle \: is \: \pmb{\bf 16 \: m \:\& \: 33 \:m \:}\:, respectively. \:}\\\\ \end{gathered}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━

⠀⠀⠀

${\textsf{\textbf{\orange{@ItzAakriti♡}}}}$