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An Olympic pool is rectangular with a length of 50 meters. Ms Burri wants to fit an Olympic pool in her backyard but doesn't have enough room so she plans to build a similar pool with a length of only 30 meters.

a. She wants to replace the pool deck around her new smaller pool. What is the ratio of the perimeter of the Olympic pool to the new smaller pool?

b. The area of the olympic pool is 1,2500 meters squared. If she were to buy a pool cover to fit her brand new smaller pool, what would the area be?

Respuesta :

Perimeter of older

  • 2(50+W)
  • 100+2W

Perimeter of newer

  • 2(30+W)
  • 60+2W

As w is constant cancel it

Ratio

  • 100/60
  • 5/3

Ratio of area is also same

So

  • 5/3=12500/x
  • 5x=37500
  • x=37500/5
  • x=7500m²

Answer:

See below ~

Step-by-step explanation:

Finding perimeter of Olympic pool and regular pool :

  • P (olympic) = 2(l + w) = 2(50 + w) = 2w + 100
  • P (regular) = 2(l + w) = 2(30 + w) = 2w + 60

Taking the ratio :

  • 2w + 100 : 2w + 60
  • 100 : 60
  • 5 : 3

Using ratios to find area of regular :

  • 5 : 3 = 12,500 : a
  • a = 12500/5 x 3 = 2500 x 3
  • a = 7,500 m²