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A rectangular sheet PQRS is such that PQ = 6 and QR = 8.  It is folded so that corner P goes to corner R.  Find the length of the crease.

Jun 17, 2020

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A rectangular sheet PQRS is such that PQ = 6 and QR = 8.  It is folded so that corner P goes to corner R.

Find the length of the crease.

$$\begin{array}{|rclrclrcl|} \hline \tan(\psi) &=& \dfrac{6}{8} & &=& & \tan(\psi) &=& \dfrac{x}{\sqrt{6^2+8^2}} \\\\ && &\dfrac{6}{8} &=& \dfrac{x}{\sqrt{6^2+8^2}} \\\\ && &\dfrac{6}{8} &=& \dfrac{x}{10} \\\\ && & x &=& \dfrac{6*10}{8} \\\\ && & x &=& \dfrac{60}{8} \\\\ &&& \mathbf{x} &=& \mathbf{7.5 } \\ \hline \end{array}$$

The length of the crease is $$\mathbf{7.5 }$$

Jun 18, 2020