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The length of a new rectangular playing field is 3 yards longer than double the width. If the perimeter of the rectangular playing field is ​252 yards, what are its​ dimensions?

Respuesta :

Answer:

Given:

  • Length of a rectangular field is 3 yards longer than double the breadth.
  • Perimeter is 252 yards.

[tex] \: [/tex]

To Find:

  • It's dimensions?

[tex] \: [/tex]

Solution:

Let,

  • Breadth be 'b'

So,

length will be 2b + 3

[tex] \: [/tex]

As, we know:

[tex] \bigstar \quad {\underline{ \boxed{ \green{Perimeter = 2 ( length + breadth ) }}}} \quad \bigstar[/tex]

➝ 2[(2b + 3) + b)] = 252

➝ 2( 3b + 3 ) = 252

➝ 6b + 6 = 252

➝ b + 1 = 42

➝ b = 41

[tex] \: [/tex]

Now putting the value of b in second equation:

➝ l = 2(41) + 3 = 85

[tex] \: [/tex]

Hence,

  • Width is 41 yards
  • length is 85 yards

[tex] \: [/tex]

Check:

2( l+b ) = 252

➝ 2( 85 + 41 )

➝ 2( 126 )

➝ 252

_____________________

Additional Information:

[tex] \: \: \: \: \: \: { \sf{ \mathbb{ \pink{Formula's \: for \: Perimeter}}}}[/tex]

★ Triangle = Sum of all sides

★ Square = 4 × Side

★ Rectangle = 2( l + b )

★ Circle = 2πr

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