Question

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

Answer 1

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

$2(4W + 9 + W) = 528$

• Add like terms

$2(5W + 9) = 528\\\\10W + 18 = 528$

• Subtract 18 from each side

$10W = 528 - 18\\\\10W = 510$

• 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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