What is the ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half is similar to the original rectangular sheet? Express your answer as a common fraction in simplest radical form. (Assume the width of the original sheet of paper becomes the length of the folded sheet.)

The ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half is similar to the original rectangular sheet is (√2):1.

What is a Ratio?

A ratio expresses the number of times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, while the orange to total fruit ratio is 8:14.

When the paper is not folded or can be said that the paper is in its initial form. Therefore, the dimension of the paper can be written as,

Length = x

Width = y

Now, the paper is folded such that the width of the original sheet of paper becomes the length of the folded sheet, and the width of the folded sheet is half the length of original sheet. Therefor, the dimension of the folded sheet are,

Length of the folded sheet = y

Width of the folded sheet = x/2

Further, the ratio of the rectangles can be written as,

Length/Width = x/y = y/(x/2)

x/y = 2y/x

x²/y² = 2/1

x/y = (√2)/1

Hence, the ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half is similar to the original rectangular sheet is (√2):1.

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