Question

A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 1

`√(170) in` is the answer

Explanation:

AC to the diagram AC is the diagonal of ABCD so:

`AC^2` =
`AB^2` +
`BC^2`

For ΔACP,
`AP^2` =
`AC^2` +
`PC^2`

`AP^2` =
`AB^2` +
`BC^2` +
`PC^2`

=
`5^2` +
`8^2` +
`9^2`

= 170

`√(170) in` being the answer