# A standard piece of paper is 8.5 inches by 11 inches. A piece of legal-size paper is 8.5 inches by 14 inches. By what scale factor k would you need to dilate the standard paper so that you could fit two pages on a single piece of legal paper?

Question
A standard piece of paper is 8.5 inches by 11 inches. A piece of legal-size paper is 8.5 inches by 14 inches. By what scale factor k would you need to dilate the standard paper so that you could fit two pages on a single piece of legal paper?

2020-12-26
You would need that the length of the standard paper be equal to the width of the length of the legal paper. Hence, the scale factor must be the ratio of the width of the legal paper to the length of length of the standard paper: $$\displaystyle{k}=\frac{{8.5}}{{11}}=\frac{{17}}{{22}}$$
To check if the widths of the two dilated standard papers fit along the length of the legal paper, we multiply the scale factor to 2 times the width of the standard paper:
$$\displaystyle{2}\cdot{\left(\frac{{17}}{{22}}\right)}{\left({8.5}\right)}\sim{13.1}\in.{<}{14}\in$$</span>
So, the two pages will fit for this value of k.

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