Final answer:
The width of the table is 2 meters and the length is 6 meters. The length of the lace border is 20 cm. Therefore, the length of the lace border is 20 cm.
Step-by-step explanation:
First, we can let the width of the table be represented by x meters.
Since the length is three times the width, we can express the length as 3x meters.
The area of the table can be calculated by multiplying the length and the width, which gives us the equation (3x)(x) = 12.
To solve for x, we can divide both sides of the equation by 3, giving us x^2 = 4.
Taking the square root of both sides, we find x = 2.
Therefore, the width of the table is 2 meters and the length is 6 meters.
The table cloth hangs 20 cm on each side, so we need to add 20 cm to both the length and the width of the table. Therefore, the length of the table cloth is 6 + 20 + 20 = 46 cm.
To find the length of the lace border, we subtract the original length of the table from the
length of the table cloth, which gives us 46 - 6 = 40 cm.
However, the question asks for the length of the lace border, so we divide the total length of the lace border by 2 to account for both sides of the table, giving us 40 / 2 = 20 cm.
Therefore, the length of the lace border is 20 cm.