Answer: 6 ft ^ 2
Step-by-step explanation:
We have been given that a piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide.
First of all, let us find the scale factor by which the width of the carpet has been reduced.
<em>Original width of carpet x scale factor = 12</em>
<em>Dividing both sides by 8 feet we will get:</em>
<u><em>8 feet x Scale factor/8 ft = 2/8 ft</em></u>
<em>Scale Factor = 1/4 </em>
<em>Let us find the length of carpet after reduced by a scale factor of 1/4. </em>
Length of the carpet after reducing a factor of 1/4=12 ft x 1/4
Length of the carpet after reducing a factor of 1/4=3 ft.
Now we will multiply the reduced length and width of the carpet to find the area of reduced carpet.
Area of reduced carpet = 2 ft x 3 ft
Area of reduced carpet = 6 ft
Therefore, the area of reduced carpet is 6 square feet.
.