Question

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

Answer 1

• 32 square feet

• 20 square feet

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