Question

The area of rectangle is 105cm2.if its length is 21 cm, what is its breadth and perimeter

Answer 1

Answer:

• breadth = 5cm
• perimeter = 52 cm

Step-by-step explanation:

$\bold{ \boxed{ \huge \mathfrak{ \colorbox{gray}{Given : - }}}}$

$\: \: \: \: \: : \implies \: area \: of \: rectangle = 105 \: {cm}^{2}$

$\: \: \: \: \: : \implies \: length \: of \: rectangle = 21 \: cm$

$\color{blue}\bold{ \boxed{ \huge \mathfrak{ \colorbox{pink}{To find:-}}}}$

$\: \: \: \: \: : \implies \: perimeter \: of \: rectangle$

$\: \: \: \: \: : \implies \: breadth \: of \: rectangle$

$\mathfrak{We \: know \: that : - }$

$\: \: \: \: \: \implies \: area \: of \: rectangle \: = length \times breadth = 105 \: {cm}^{2}$

$\: \: \: \: \: \implies 21\times breadth = 105 \:$

$\: \: \: \: \: \implies breadth = \frac{105}{21}$

$\: \: \: \: \: \implies breadth = 5 \: cm$

$\mathfrak{We \: also \: know \: that : - }$

$\: \: \: \: \: \implies \: perimeter \: of \: rectangle = 2(length + breadth)$

$\: \: \: \: \: \implies2( 21 + 5) =52 \: cm$

$Hence \: the \: perimete r \: and \: breadth \: of \: rectangle \: is \: 5 \: and \: 52 \: cm \: respectively$

Answer 2

Given that , The area of rectangle is 105cm² and it's length is 21 cm ..

Need To Find : The Breadth & Perimeter of Rectangle ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Breadth of the Rectangle be x cm .

As , We know that ,

⠀⠀⠀⠀⠀▪︎⠀Formula for Area of Rectangle :

$\qquad \star \large\:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Area _{(\:Rectangle \:)}\:\:=\:Length \:\times \:Breadth \: \:\:sq.units\:}}}}}$

⠀⠀⠀⠀⠀Here , Length of Rectangle is 21 cm & Area of Rectangle is 105 cm² .

$\qquad \dashrightarrow \sf \:\:Area _{(\:Rectangle \:)}\:\:=\:Length \:\times \:Breadth \: \:$

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

$\qquad \dashrightarrow \sf \:\:Area _{(\:Rectangle \:)}\: \:=\:Length \:\times \:Breadth \: \:\\\\\qquad \dashrightarrow \sf \:\:105\:\:=\:21 \:\times \:x \: \:\\\\\qquad \dashrightarrow \sf \: \:x \:=\:\dfrac{105}{21}\: \:\\\\\qquad \dashrightarrow \sf \: \:x \:=\:\cancel{\dfrac{105}{21}}\: \:\\\\\qquad \dashrightarrow \sf \: \:x \:=\:5\: \:\\\\\dashrightarrow \underline {\boxed{\pmb{\frak{\purple {\:x \:=\:5\:cm\: }}}}}\:$

Therefore,

• Breadth of Rectangle is x = 5 cm .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Perimeter of Rectangle :

As , We know that ,

⠀⠀⠀⠀⠀▪︎⠀Formula for Perimeter of Rectangle :

$\qquad \star \large\:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Perimeter _{(\:Rectangle \:)}\:\:=2 \:( \:Length \:+ \:Breadth \: )\:\:units\:}}}}}$

⠀⠀⠀⠀⠀Here , Length of Rectangle is 21 cm & Breadth of Rectangle is 5 cm .

$\qquad \dashrightarrow \sf \:\: \:\:Perimeter _{(\:Rectangle \:)}\:\:=2 \:( \:Length \:+ \:Breadth \: )\: \: \:$

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

$\qquad \dashrightarrow \sf \:\: \:\:Perimeter _{(\:Rectangle \:)}\:\:=2 \:( \:Length \:+ \:Breadth \: )\: \: \:\\\\\qquad \dashrightarrow \sf \:\: \:\:Perimeter _{(\:Rectangle \:)}\:\:=2 \:( \:21 \:+ 5 \: )\:\: \:\\\\\qquad \dashrightarrow \sf \:\: \:\:Perimeter _{(\:Rectangle \:)}\:\:=2 \:( \:26 \: )\:\: \:\\\\\qquad \dashrightarrow \sf \:\: \:\:Perimeter _{(\:Rectangle \:)}\:\:=\:52\: \:\\\\\dashrightarrow \underline {\boxed{\pmb{\frak{\purple {\:\:\:\:Perimeter _{(\:Rectangle \:)}\:\:=\:52\:cm }}}}}\:$

$\qquad \therefore \underline {\sf Hence, \:The \:Perimeter \:of\:Rectangle \: is \:\pmb{\bf 52 \: cm \:}\:.\:}$