ANSWER
[tex]9.4in[/tex]EXPLANATION
First, let us make a sketch of the problem:
The envelope is shaped like a rectangle.
The maximum possible length of the pencil is the length of the diagonal of the envelope.
To find the length of the diagonal, apply the Pythagoras theorem:
[tex]\text{hyp}^2=a^2+b^2[/tex]where hyp = hypotenuse
a, b = legs of the triangle formed by the diagonals and the sides of the envelope.
Therefore, for the question, we have that:
[tex]\begin{gathered} p^2=5^2+8^2 \\ p^2=25+64 \\ p^2=89 \\ p=\sqrt[]{89} \\ p\approx9.4in \end{gathered}[/tex]The maximum possible length of the pencil is 9.4 inches.
