The 42 inches fishing rod is fit into the box.
Explanation:
Length of the box = 40 inch
Width of the box = 10 inch
Height of the box = 10 inch
Let us first find the diagonal of the base of the box and 'd' be the diagonal.
Diagonal formula:
[tex]d^2=l^2+w^2[/tex]
[tex]=40^2+10^2[/tex]
[tex]=1600+100[/tex]
[tex]d^2=1700[/tex]
Let r be the length from a bottom corner to the opposite top corner.
To find r:
Using Pythagoras theorem,
[tex]r^2=s^2+h^2[/tex]
[tex]=1700+10^2[/tex]
[tex]=1700+100[/tex]
[tex]r^2=1800[/tex]
Taking square root on both side of the equation,
[tex]r=\sqrt{1800}[/tex]
r ≈ 42.43 inch
The length of the longest tube that will fit in the box is 42.43 inches.
Hence the 42 inches fishing rod is fit into the box.
