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The length of a rectangle is 3 m less than twice the width, and the area of the rectangle is 27 m. Find the dimensions of the rectangle.​

Respuesta :

mhanifa

Answer:

  • 4.5 m and 6 m

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Let the length be l and width be w.

Given:

  • l = 2w - 3,
  • A = lw = 27.

Substitute l and solve for w:

  • lw = 27
  • w(2w - 3) = 27
  • 2w² - 3w = 27
  • 2w² - 3w - 27 = 0
  • 2w² - 9w + 6w - 27 = 0
  • w(2w - 9) + 3(2w - 9) = 0
  • (2w - 9)(w + 3) = 0
  • 2w - 9 = 0 and w + 3 = 0
  • 2w = 9 and w = - 3 (discarded as distance can't be negative)
  • w = 4.5

Find the value of l:

  • l = 2*4.5 - 3 = 9 - 3 = 6

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