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Question 66
Parallel lines are drawn on a rectangular piece of paper, The paper is then cut along each of, the lines, forming n identical rectangular strips. If the strips have the same ratio of length to width as the original paper, this ratio is
Solution
Let the length of each small rectangular strips is 'l' and its breadth is 'b'.
Breadth of piece of paper = Length of each small strips = l
Length of piece of paper = Sum of breadth of 'n' small strips = nb
Now,
$$\frac{l}{b} = \frac{nb}{l}$$
$$l^{2} = nb^{2}$$
$$l = \sqrt{n}b$$
$$l: b = \sqrt{n}: 1$$
