Question

Tim takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 10 inches long and the width of the paper is 9 inches. What is the paper's length?

Answer 1

In a diagram, this is the information we have

Notice that, after cutting the sheet of paper, we get 2 right triangles.

We can use the Pythagorean theorem to find the length of the paper as follows:

`\begin{gathered} (10in)^2=(9in)^2+(length)^2 \\ \Rightarrow\text{length}=\sqrt[]{(10in)^2-(9in)^2}^{} \\ \Rightarrow\text{length}=\sqrt[]{19in^2} \\ \Rightarrow\text{length}=\sqrt[]{19}in \end{gathered}`

The answer is sqrt(19) in, which is, approximately, 4.36 in