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the length of a new rectangular playing field.is 9 yards longer than quadruple the width, If the perimeter of the rectangular playing field is 528 yards what are its dimensions

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akposevictor

The dimensions of a playing field that has a perimeter of 528 yards are:

  • Length = 213 yards
  • Width = 51 yards

Recall:

Perimeter of a rectangle = 2(L + W)

We can represent the length and width using variables to form algebraic expressions as follows:

  • Let W represent the width

  • Width = W
  • Length = (4W + 9) yards

  • Perimeter = 528 yards

The following equation would be created to find the value of W:

2(L + W) = Perimeter

  • Substitute

2[(4W + 9) + W} = 528

  • Solve for W

[tex]2(4W + 9 + W) = 528\\\\[/tex]

  • Add like terms

[tex]2(5W + 9) = 528\\\\10W + 18 = 528\\[/tex]

  • Subtract 18 from each side

[tex]10W = 528 - 18\\\\10W = 510[/tex]

  • Divide both sides by 10

W = 51

Width is the rectangular playing field is 51 yards

Find the Length:

Length = (4W + 9) yards

  • Plug in the value of W

Length = 4(51) + 9 = 213 yards

Therefore, the dimensions of a playing field that has a perimeter of 528 yards are:

  • Length = 213 yards
  • Width = 51 yards

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