The length of the interior diagonal of the box is [tex]\[34.46\text{ inches}\][/tex].
What is Pythagoras theorem?
In right triangles, the sum of the squares of the two legs [tex]$a$[/tex] and [tex]$b$[/tex] is equal to the square of the hypotenuse [tex]$c$[/tex].
[tex]a^{2} +b^{2} =c^{2}[/tex]
It is given that, a box has a base of [tex]\[12\text{ inches}\][/tex] by [tex]\[12\text{ inches}\][/tex] and height [tex]\[30\text{ inches}\][/tex].
We need to find the length of the interior diagonal of the box.
Now, we will find the length of the interior diagonal of the box by using the Pythagorean theorem.
So,
The square of the length required is,
[tex]${{\left( 12 \right)}^{2}}+{{\left( 12 \right)}^{2}}+{{\left( 30 \right)}^{2}}=1188$[/tex]
Now, we calculate the square root of [tex]1188[/tex].
[tex]$\sqrt{1188}=34.46$[/tex]
Hence, [tex]\[34.46\text{ inches}\][/tex] are the length of the interior diagonal of the box.
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