Question

the length of a rectangle is three times its width. If the perimeter is 24 cm, what is the length

Answer 1

Answer :

• Length of rectangle is 9cm

Given :

• The length of a rectangle is three time its width
• Perimeter of rectangle = 24cm

To find :

• Length

Solution :

• Let the breadth of rectangle be x

As we know that,

• Perimeter of rectangle = 2(l + b)

》24 = 2(3 + x)

》3 + x= 24/2

》4x = 12

》12 = 4x

》x = 12/4

》x = 3cm

So,

• Length of rectangle = 3x = 3(3) = 9cm
• Breadth of rectangle = x = 3cm

Hence, Length of rectangle is 9cm

Verification :

As we know that,

• Perimeter of rectangle = 2(l + b)

》2(9 + 3)

》2(12)

》24cm

Answer 2

Given : The length of a rectangle is three times its width & the perimeter is 24 cm .

Need To Find : Length of Rectangle.

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❍ Let's Consider the Width of Rectangle be x cm .

Given that,

• Length of a rectangle is three times its width.

Then ,

• Length of Rectangle is 3x cm .

$\dag\frak{\underline {As,\:We\:know\:that\::\:}}$

$\dag\:\:\boxed {\sf{ Perimeter _{(Rectangle)} =\bigg( 2 ( l + w ) \bigg)\:units}}$

Where,

• l is the Length of Rectangle and w is the Width of Rectangle .

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

$\qquad :\implies \sf { 24 = 2 ( 3x + x ) }\\\\:\implies \sf { \cancel {\dfrac{24}{2} }= 3x + x }\\\\:\implies \sf { 12 = 3x + x }\\\\:\implies \sf { 12 = 4x }\\\\:\implies \sf { \cancel {\dfrac{12}{4}}= x }\\\\:\implies \bf { x = 3cm }$

• Length of Rectangle is 3x = 3 (3) = 9 cm

• Width of Rectangle is x = 3 cm .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Length \:of\:Rectangle \:is\:\bf{9\: cm}}}}$

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V E R I F I C A T I O N :

$\dag\frak{\underline {As,\:We\:know\:that\::\:}}$

$\dag\:\:\boxed {\sf{ Perimeter _{(Rectangle)} =\bigg( 2 ( l + w ) \bigg)\:units}}$

Where,

• l is the Length of Rectangle and w is the Width of Rectangle .

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: found \: Values \::}}$

$\qquad :\implies \sf { 24 = 2 ( 9 + 3 ) }\\\\:\implies \sf { 24 = 2 ( 12 ) }\\\\:\implies \bf { 24cm = 24 cm }$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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