Question

Gina's mother has plans to carpet a floor with a width of 35 feet and a length of 50 feet. A 1.5-foot border of carpet around the room will be a different color than the rest of the carpet, as shown below. What is the area of the floor that is surrounded by the border?

Answer 1

Answer: 1504 square feet

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Step-by-step explanation:

For the larger rectangle, the bottom length is 50 ft. Subtract off two copies of 1.5 to get 50-1.5-1.5 = 47 ft, which is the bottom length of the smaller rectangle. We subtract off two copies of 1.5 as there are two sides (left and right) of a border that is 1.5, which is not part of the smaller rectangle.

The same is done for the vertical component. We start with 35 as the larger vertical side and it goes to 35-1.5-1.5 = 32

The smaller rectangle has dimensions 47 ft by 32 ft. The area is 47*32 = 1504 square feet. We can write "square feet" as "ft^2" without the quotes. Another abbreviation is "sq ft".

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Side note: the area of just the border is equal to the difference of the areas of the larger and smaller rectangle.

The larger rectangle has area 50*35 = 1750 sq ft, so the area of just the border only is 1750 - 1504 = 246 sq ft