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The diagram below shows the dimensions of Adrian's living room rug (8x4 feet). he plans to buy a new rug that is x feet longer and x feet wider. how many square feet of floor space will Adrian's new rug cover? What value of x will result in a rug with an area of 96 square feet?

Answer :

fichoh

The space covered by Adrian's new rug and the the value of x will be x² + 12x + 32 and 4 feets respectively.

Initial dimension of living room rug :

  • 8 feets by 4 feets

Increase in the length and width by x :

  • New length = 8 + x
  • New weight = 4 + x

Area of new rug = Length × width

  • (8+x) × (4+x) = 32+8x+4x+x²

The square feet of floor space covered by the new rug will be :

  • x² + 12x + 32

Value of x if rug has an area of 96 ft² :

x² + 12x + 32 = 96

x² + 12x + 32 - 96 = 0

x² + 12x - 64 = 0

factorize :

x² + 16x - 4x - 64 = 0

x(x + 16) -4(x + 16)

(x + 16) = 0 or (x - 4) = 0

x = - 16 or x = 4

Length can't be nagative ; hence the value of x will be 4

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