find the length of overline{hk} for square g h j k.
the length of overline{hk} is
(type an integer or decimal rounded to one decimal place as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Recall the property of a square
In a square $ GHJK $, all sides are equal. Let $ GH = HJ=JK = KG = 12 $.
## Step2: Apply the Pythagorean theorem
For right - triangle $ GHK $, where $ \angle{GHK}=90^{\circ}$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. Here $a = GH = 12$, $b=HK = 12$ (sides of the square), and $c=\overline{GK}$ (the diagonal we want to find).
$$
\begin{align*}
\overline{GK}&=\sqrt{GH^{2}+HK^{2}}\
&=\sqrt{12^{2}+12^{2}}\
&=\sqrt{144 + 144}\
&=\sqrt{288}\
&=\sqrt{144\times2}\
& = 12\sqrt{2}\
&\approx12\times1.414\
&=16.968\approx17.0
\end{align*}
$$

# Answer:
$17.0$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the property of a square

Step2: Apply the Pythagorean theorem

Answer: