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. What is the area of the reduced carpet?
6 square feet
12 square feet
24 square feet
48 square feet
8/x = 2.
X = 4 = Scale factor.
Area = 8/4 * 12/4 = 6 Ft^2.
To find out the area of the reduced carpet, we need to determine the scale factor first. The scale factor is the ratio of the width of the reduced carpet to the original width of the carpet.
Given:
Width of the original carpet = 8 feet
Width of the reduced carpet = 2 feet
Scale factor = Width of the reduced carpet / Width of the original carpet
Scale factor = 2 feet / 8 feet
Scale factor = 1/4
Now, we need to find the length of the reduced carpet. To do this, we multiply the original length of the carpet by the scale factor.
Length of the original carpet = 12 feet
Length of the reduced carpet = Length of the original carpet x Scale factor
Length of the reduced carpet = 12 feet x 1/4
Length of the reduced carpet = 3 feet
Finally, we can find the area of the reduced carpet by multiplying the width and length of the reduced carpet.
Area of the reduced carpet = Width of the reduced carpet x Length of the reduced carpet
Area of the reduced carpet = 2 feet x 3 feet
Area of the reduced carpet = 6 square feet
Therefore, the area of the reduced carpet is 6 square feet.
To find the area of the reduced carpet, we can use the concept of scale factor.
First, let's calculate the scale factor. The original width of the carpet is 8 feet, and the reduced width is 2 feet. Therefore, the scale factor is 2/8 or 1/4.
To find the length of the reduced carpet, we can multiply the original length by the scale factor. The original length is 12 feet, so the length of the reduced carpet is 12 * (1/4) = 3 feet.
Now, we can calculate the area of the reduced carpet by multiplying the width and length. The width is 2 feet and the length is 3 feet, so the area is 2 * 3 = 6 square feet.
Therefore, the area of the reduced carpet is 6 square feet.