# 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?

Mar 12, 2017

See the entire solution process below:

#### Explanation:

First, we can use the Pythagorean Theorem to find the length of the $\textcolor{red}{red}$ 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 $\textcolor{g r e e n}{g r e e n}$ 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.