The length of the longest metal rod that can be sent is 12 inches.
As given, the only boxes available for shipping are 7-inch cubes. As Jorge needs to ship a thin metal rod to a metalworking shop, he will put the rods diagonally or space diagonally in the box.
The space diagonal of a cube can be found by the formula :
[tex]D=\sqrt{x^{2}+x^{2}+x^{2} }[/tex]
= [tex]\sqrt{3} x[/tex]
Here, x is 7 inches.
So, Diagonal is = [tex]\sqrt{3} \times7[/tex]
= [tex]1.732\times7=12.12[/tex] inches.
Rounding this to nearest whole number we get 12.
So, the length of the longest metal rod that can be sent is 12 inches.
