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a school playground is rectangular and has a length of 50 m and a width of 30m as shown. A safety zone of uniform width surrounds the playground. If the area of the safety zone equals the area of the playground, what is the width of the safety zone to 2 decimal places

Respuesta :

mhanifa

Answer:

  • 7.84 m

Step-by-step explanation:

Area of the playground:

  • 50*30 = 1500 m²

Let x m added as safety zone to each length and width, then the area including safety zone is:

  • (2x + 50)(2x + 30) = 1500*2

Solving for x:

  • 4x² + 160x  + 1500 = 2*1500
  • 4x² + 160x - 1500 = 0
  • x² + 40x - 375 = 0
  • x² + 2*20x + 400 = 775
  • (x + 20)² = 775
  • x + 20 = √775
  • x = √775 - 20
  • x = 7.84 m rounded to 2 decimal places

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