Question

9.
The length of a rectangular field is 8 meters less than twice its breadth. If the perimeter
the rectangular field is 56 meters, find its length and breadth?​

Answer 1

Given : The length of a rectangular field is 8 meters less than twice its breadth & the perimeter the rectangular field is 56 m .

Need To Find : Length & Breadth of Rectangular field.

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❍ Let's Consider b be the Breadth of Rectangular field.

Given that ,

• The length of a rectangular field is 8 meters less than twice its breadth.

Then ,

• Length of Rectangular Field is 2b - 8 .

As, We know that ,

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

Where,

• l is the Length of Rectangular field and b is the Breadth of Rectangular field.

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

$\qquad:\implies \sf{ 56 = 2( b + 2b - 8 ) }$

$\qquad:\implies \sf{ \cancel {\dfrac{56}{2}} = b + 2b - 8 }$

$\qquad:\implies \sf{ 28 = b + 2b - 8 }$

$\qquad:\implies \sf{ 28 + 8= b + 2b }$

$\qquad:\implies \sf{ 36 = b + 2b }$

$\qquad:\implies \sf{ 36 = 3b }$

$\qquad:\implies \sf{ b\:= \:\cancel {\dfrac{36}{3}} }$

$\qquad:\implies \bf{b = 12 m }$

Therefore,

• Breadth of Rectangular field is x = 12 m
• Length of Rectangular features is (2x - 8) = ( 12 × 2 - 8) = 24 - 8 = 16 m

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {Hence \:The\:Length \:and\:  Breadth \:of\:Rectangular \:Field \:is\:\bf{12\: m\:and\:16m\: } \:\: respectively. }}}$

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

As, We know that ,

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

Where,

• l is the Length of Rectangular field and b is the Breadth of Rectangular field.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Found \: Values \::}}$

$\qquad:\implies \sf{ 56 = 2( 16 + 12 ) }$

$\qquad:\implies \sf{ 56 = 2( 28 ) }$

$\qquad:\implies \bf{ 56 m= 56m }$

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

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Answer 2

Answer :-

• Length of the rectangular field = 16 m.
• Breadth of the rectangular field = 12 m.

Given :-

• The length of a rectangular field is 8 metres less than twice it's breadth.

• The perimeter of the rectangular field is 56 metres.

To find :-

• The length and breadth of the rectangular field.

Step-by-step explanation :-

• In this question, it has been given that the length of a rectangular field is 8 metres less than twice it's breadth. It has also been given that the perimeter of the rectangular field is 56 metres. We have to find it's length and breadth.

• The field is in the shape of a rectangle, since it's a rectangular field. So, we are going to use the formula required for finding the perimeter of a rectangle and find out our answer.

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Calculations :-

• Let the breadth of the rectangular field be x.

• Twice the breadth = 2x.

• It has been given that the length is 8 metres less than twice it's breadth, so we have to subtract 8 metres from 2x.

• 8 metres less than twice it's breadth = 2x - 8. So the length is 2x - 8.

• The perimeter of the field is 56 metres.

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We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Here,

• Length = 2x - 8.
• Breadth = x.

• Perimeter = 56 metres.

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$\underline{\underline{ \mathfrak{Substituting \: these \: values \: in \: this \: formula,}}}$

$\tt56 = 2 \: (2x - 8 + x)$

Removing the brackets by simplifying,

$\tt56 = 4x - 16 + 2x$

Transposing 16 (constant) from RHS to LHS, changing it's sign,

$\tt56 + 16 = 4x + 2x$

Adding 16 to 56,

$\tt72 = 4x + 2x$

Adding 2x to 4x,

$\tt72 = 6x$

Transposing 6 from RHS to LHS, changing it's sign,

$\tt\dfrac{72}{6} = x$

Dividing 72 by 6,

$\overline{\boxed{\tt12 \: m = x}}$

• The value of x is 12.

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Hence, the dimensions of the rectangular field are as follows :-

$\sf Length = 2x - 8$

Substituting the value of x,

$\sf Length = 2 \times 12 \: m - 8$

Applying BODMAS rule and multiplying 2 by 12 first,

$\sf Length = 24 \: m - 8$

Subtracting 8 from 24,

$\underbrace{\boxed{\sf Length = 16 \: m}}$

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$\sf Breadth = x$

Substituting the value of x,

$\underbrace{ \boxed{\sf Breadth = 12 \: m}}$

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$\underline{\underline{\rm Abbreviations \: used :-}}$

L = Length.

B = Breadth.