a straw is placed inside a rectangular box that is 1 inches by 1 inches by 2 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 attempt 1 out of 2 in. submit answer

Question

Accepted Answer

# Explanation:
## Step1: Find the diagonal of the base
The base is a square with side length $a = 1$ inch. Using the Pythagorean theorem $d_{base}^2=a^{2}+a^{2}$.
$$
\begin{align*}
d_{base}^2&=1^{2}+1^{2}\
d_{base}^2&=1 + 1\
d_{base}^2&=2\
d_{base}&=\sqrt{2}
\end{align*}
$$
## Step2: Find the space - diagonal (length of the straw)
Let the height of the box $h = 2$ inches. Using the three - dimensional Pythagorean theorem $d_{space}^2=d_{base}^2+h^{2}$.
Substitute $d_{base}^2 = 2$ and $h = 2$ (so $h^{2}=4$) into the formula:
$$
\begin{align*}
d_{space}^2&=2+4\
d_{space}^2&=6\
d_{space}&=\sqrt{6}
\end{align*}
$$

# Answer:
$\sqrt{6}$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the diagonal of the base

Step2: Find the space - diagonal (length of the straw)

Answer: