Question

The perimeter of a rectangular play ground is 280 meter and its length is 2 meters more than twice its breadth . Find the length and breadth of the play ground

Answer 1

Answer:

The Length of playground = 94 meter

The Breadth of playground = 46 meter

Step-by-step explanation:

Let,

The Breadth of rectangular play ground = x

The Length of rectangular play ground = 2x + 2

The perimeter of a rectangular play ground is 280 meter

Perimeter = 2 (Length + Breadth)

⇒ 280 = 2 (2x + 2 + x)

⇒ 280 = 4x + 4 + 2x

⇒ 280 = 4x + 2x + 4

⇒ 280 = 6x + 4

⇒ 280 - 4 = 6x

⇒ 276 = 6x

⇒ x = 276 / 6

⇒ x = 46

The Breadth of rectangular play ground = 46 meter

The Length of rectangular play ground = 2x + 2

⇒ 2 (46) + 2

⇒ 94

The Length of rectangular play ground = 94 meter

Therefore, the Length of playground = 94 meter and the Breadth of playground = 46 meter.

Answer 2

Given that , The perimeter of a rectangular play ground is 280 meter and it's length is 2 meters more than twice its breadth .

Need To Find : The length and breadth of the play ground ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

As , We know that ,

• Formula for PERIMETER of RECTANGLE :

$\qquad \dag\:\:\bigg\lgroup \pmb{\sf { \:\:Perimeter _{(Rectangle)} \:: 2( l +  b ) \:units\: }\bigg\rgroup$

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

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that Breadth of Rectangular playground be a meters .

⠀⠀⠀⠀⠀Given that,

• The Length of Rectangular Playground is 2 meters more than twice its breadth .

Therefore,

• Length of Rectangular Playground is ( 2a + 2 ) meters .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\qquad \underline {\underline {\:\:\purple {\bf { \:\:\bigstar \:\: Finding \: Length \:and \:Breadth \:of \:Rectangular \:Field \:\:: \:}}}}$

$\qquad \dashrightarrow \sf \: \:\:Perimeter _{(Rectangle)} \:= 2( l +  b ) \:units\: \:$

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

• The Perimeter of Rectangular Playground is 280 m .

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

$\qquad \dashrightarrow \sf \: \:\:280 \:= 2\Big\{ \: ( 2a + 2 ) +  a \Big\} \:\: \:$

$\qquad \dashrightarrow \sf \: \:\:\cancel{\dfrac{280}{2}} \:= \Big\{ \: ( 2a + 2 ) +  a \Big\} \:\: \:$

$\qquad \dashrightarrow \sf \: \:140 \:= \Big\{ \: 2a + 2 +  a \Big\} \:\: \:$

$\qquad \dashrightarrow \sf \: \:140 - 2 \:= \Big\{ \: 2a +  a \Big\} \:\: \:$

$\qquad \dashrightarrow \sf \: \:138 \:= \Big\{ \: 2a +  a \Big\} \:\: \:$

$\qquad \dashrightarrow \sf \: \:138 \:= \: 3a \:\: \:$

$\qquad \dashrightarrow \sf \: \:a \:= \: \cancel{\dfrac{138}{3}} \:\: \:$

$\qquad \dashrightarrow \sf \: \:a \:= \: 46 \:\: \:$

$\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\pink{\: \:a \:= \: 46 \:m \:}}}}} \:\: \:$

Therefore,

• Breadth of Rectangular Field is a = 46 m .
• Length of Rectangular field is ( 2a + 2 ) = ( 2 (46) + 2 ) = 94 m .