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James is building a house on the lot shown below. The dimensions of the lot are (6+x) feet and (6−x) feet. The blue prints show the dimensions of the house to be (2+x) feet and (2−x) feet. The rest of the lot will be his yard.

How large is the yard?
square feet

James is thinking about extending the house by adding 2 feet to the length and 2 feet to the width.

How much area is now left for the yard?
square feet

Respuesta :

mhanifa

Answer:

  • 32 square feet
  • 20 square feet

Step-by-step explanation:

Given

  • The dimensions of the lot are (6+x) feet and (6−x) feet
  • The dimensions of the house to be (2+x) feet and (2−x) feet

Area of the yard = Area of the lot - Area of the house

Area of the yard:

  • (6 + x)(6 - x) - (2 + x)(2 - x) =
  • 36 - x² - 4 + x² =
  • 32 square feet

If the house is extended, then the area of the yard will change as:

  • (6 + x)(6 - x) - (4 + x)(4 - x) =
  • 36 - x² - 16 + x² =
  • 20 square feet

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