Question

the length of a rectangle is 1 cm more than twice of its breadth if perimeter of the rectangle is 110 cm then find the length and breadth of rectangle​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Perimeter of rectangle = 110cm
• length of the rectangle is 1 more than the twice of its breadth .

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• length and breadth = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let the breadth be x

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ATQ :-

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length = 2x + 1

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We know that :-

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$\sf{\red{\boxed{\bold{perimeter \: of\: rectangle = 2 ( length + breadth ) }}}}$

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• putting values in the formulae

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$\sf :\implies\: {\bold{ 110 = 2( x + 2x + 1 )}}$

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$\sf :\implies\: {\bold{ 110 = 2 ( 3x + 1 )}}$

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$\sf :\implies\: {\bold{ \dfrac{110}{2} = 3x + 1 }}$

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$\sf :\implies\: {\bold{ 55 = 3x + 1 }}$

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$\sf :\implies\: {\bold{ 3x = 55 - 1 }}$

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$\sf :\implies\: {\bold{3x = 54 }}$

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$\sf :\implies\: {\bold{x = \dfrac{54}{3} }}$

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$\sf :\implies\: {\bold{x = 1 8}}$

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• Putting value of x in length and breadth

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breadth = x = 18cm

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length = 2x + 1 = 2 × 18 + 1 = 36 + 1 = 37cm

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Length and breadth of the rectangle is 18cm and 37cm

Answer 2

Step-by-step explanation:

Given

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Perimeter of rectangle = 110cm

length of the rectangle is 1 more than the twice of its breadth .

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______________________

\sf{\bold{\green{\underline{\underline{To\:Find}}}}}

ToFind

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length and breadth = ??

______________________

\sf{\bold{\green{\underline{\underline{Solution}}}}}

Solution

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let the breadth be x

⠀⠀⠀⠀

ATQ :-

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length = 2x + 1

⠀⠀⠀⠀

We know that :-

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\sf{\red{\boxed{\bold{perimeter \: of\: rectangle = 2 ( length + breadth ) }}}}

perimeterofrectangle=2(length+breadth)

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putting values in the formulae

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\sf :\implies\: {\bold{ 110 = 2( x + 2x + 1 )}}:⟹110=2(x+2x+1)

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\sf :\implies\: {\bold{ 110 = 2 ( 3x + 1 )}}:⟹110=2(3x+1)

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\sf :\implies\: {\bold{ \dfrac{110}{2} = 3x + 1 }}:⟹

2

110

=3x+1

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\sf :\implies\: {\bold{ 55 = 3x + 1 }}:⟹55=3x+1

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\sf :\implies\: {\bold{ 3x = 55 - 1 }}:⟹3x=55−1

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\sf :\implies\: {\bold{3x = 54 }}:⟹3x=54

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\sf :\implies\: {\bold{x = \dfrac{54}{3} }}:⟹x=

3

54

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\sf :\implies\: {\bold{x = 1 8}}:⟹x=18

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Putting value of x in length and breadth

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breadth = x = 18cm

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length = 2x + 1 = 2 × 18 + 1 = 36 + 1 = 37cm

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\sf{\bold{\green{\underline{\underline{Answer}}}}}

Answer

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Length and breadth of the rectangle is 18cm and 37cm