Question

A straw is place into a rectangle box that is 4 inches by 5 inches by 9 inches. If the straw fits into the box diagonally from the bottom left corner to the top right back corner, how long is the straw?

Answer 1

See the entire solution process below:

Explanation:

First, we can use the Pythagorean Theorem to find the length of the `color(red)(red)` line labelled ["c" inches]. The Pythagorean Theorem states for a right triangle, which the sides of a rectangle and the diagonal form, `a^2 + b^2 = c^2` where `a` and `b` are legs of the triangle and `c` is the hypotenuse.

Substituting for `3` for `a` and `4` for `b` and solving for `c` gives:

`3^2 + 4^2 = c^2`

`9 + 16 = c^2`

`25 = c^2`

`sqrt(25) = sqrt(c^2)`

`5 =c`

`c = 5`

We can now solve for the length of the `color(green)(green)` line which is also the length of the straw. Again, we can use the Pythagorean Theorem substituting `5` for `a` and `9` for `b` and again solving for `c`:

`5^2 + 9^2 = c^2`

`25 + 81 = c^2`

`106 = c^2`

`sqrt(106) = sqrt(c^2)`

`10.296 = c`

`c = 10.296` rounded to the nearest thousandth.

The length of the straw is `sqrt(106)` inches or `10.296` inches rounded to the nearest thousandth.