Answer:
Tthe length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2
Explanation:
To calculate the length and breadth of an A4 sheet of paper, we can use the information provided in the problem.
First, we know that the ratio of the length to the breadth is √2:1. This means that for every √2 units of length, there is 1 unit of breadth.
Next, we know that the area of the sheet is 1/6m². To find the length and breadth, we can use the formula for the area of a rectangle, which is length x breadth.
So, we can set up the equation:
(length) x (breadth) = 1/6m²
We can then use the information about the ratio of length to breadth to set up a proportion:
length/breadth = √2/1
Now we can cross-multiply and substitute this proportion into our area equation:
length x breadth = 1/6m²
length x (length/√2) = 1/6m²
length^2 = 1/6m² * √2
length = √(1/6m² * √2)
To find the breadth we can use proportionality again
breadth = length/√2
So, the length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2