Answer:
If a square has an area of 144 square inches and is reduced by a factor of 1/6, it means that both the length and width of the square are multiplied by the square root of 1/6.
To find the new side length, we can take the square root of 1/6 and multiply it by the original side length.
Original side length = sqrt(144) = 12 inches
New side length = (1/6)^(1/2) * 12 inches
Simplifying the calculation:
New side length = (1/√6) * 12 inches
Now we can calculate the new side length:
New side length ≈ 3.27 inches (rounded to two decimal places)
To find the new area, we square the new side length:
New area = (3.27 inches)^2 ≈ 10.68 square inches (rounded to two decimal places)
Therefore, after reducing the square by a factor of 1/6, the new side length is approximately 3.27 inches, and the new area is approximately 10.68 square inches.