Question

Below is a floor plan for a combined living and dining area. The owners of the home have recently adopted a puppy, so the living room needs to be re-carpeted (bad puppy). The total area for both rooms is expressed as LaTeX: 2x^2+x+3 square meters. The tile in the dining room was already replaced, so we know the area of that room is LaTeX: 2x^2-2x square meters. Find an expression for the area that needs to be re-carpeted.

Answer 1

[TeX] 3x+3[/TeX] Square metres.

Explanation:

The total area of both rooms is given as: [TeX] 2x^2+x+3[/TeX] Square Metres.

Area of the Dinning Room that was already recarpeted= [TeX] 2x^2-2x [/TeX] square meters.

Total Area=Area of Living Room+Area of Dinning Room

[TeX] 2x^2+x+3[/TeX] =Area of Living Room+[TeX] 2x^2-2x [/TeX]

Therefore:

Area of Living Room=[TeX] 2x^2+x+3-(2x^2-2x)[/TeX]

Opening the brackets

=[TeX] 2x^2+x+3-2x^2+2x[/TeX]

=[TeX] x+3+2x[/TeX]

=[TeX] 3x+3[/TeX]

Area that needs to be Carpeted=[TeX] 3x+3[/TeX] Square metres.