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A rectangular garden measures 15 meters by 24 meters. A larger garden is to be made by increasing each side by the same amount. The resulting area is to be 1.5 times the original area. Find the dimensions of the new garden to the nearest tenth to answer.

Respuesta :

mhanifa

Answer:

  • 19.2 m and 28.2 m

Step-by-step explanation:

Dimensions of a garden

  • Width = 15 m
  • Length = 24 m

Sides increase = x

New area = 1.5 times of the original

Area

  • wl = 15*24 = 360 m²

New area   (w + x)(l + x)

  • (15 + x)(24 + x) = 360*1.5
  • x^2 + 39x + 360 = 540
  • x^2 + 39x - 180 = 0

Positive root of the equation

  • x = 4.2 rounded to nearest tenth

New dimensions are:

  • 15 + 4.2 = 19.2 m
  • 24 + 4.2 = 28.2 m

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