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A rectangle patio has a perimeter of 38 feet. If the length of the patio is 5 feet less than twice the width, find the dimensions of the patio

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Chetankachanaidn

Answer:

The length is 11ft.

The width is 8ft.

Step-by-step explanation:

Hello!

Perimeter of a rectangle: [tex]P = 2(l + w)[/tex]

  • P = perimeter
  • l = length
  • w = width

We know that the length is 5 ft less than twice the width, which can be expressed by the equation: l = 2w - 5. We can plug in 38 for "P".

We can substitute the equation for l, and solve for the width.

Solve for W

  • [tex]P = 2(l + w)[/tex]
  • [tex]38 = 2((2w - 5) + w)[/tex]
  • [tex]38 = 2(3w - 5)[/tex]
  • [tex]38 = 6w - 10[/tex]
  • [tex]48 = 6w[/tex]
  • [tex]8 = w[/tex]

The width is 8. We can solve for the length by plugging it back into the equation l = 2w - 5

Solve for L

  • l = 2w - 5
  • l = 2(8) - 5
  • l = 16 - 5
  • l = 11

The length is 11.

The dimensions are 11 ft and 8 ft.

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