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Answer to first problem
Consider the top of the box which is rectangle with width 5 feet and length 4 feet.
we need to find the diagnol of this rectangle
if we draw a diagnol of this rectangle then we have two right angled triangles
for which we need to fing the hypotynuse
so the diagnol will be Sqrt(5^2 + 4^2)
= Sqrt(25 + 16)
= Sqrt(41) = 6.4 Feet
Solution to the Second Problem
Now imagine to cut the box into two halves along the calculated diagnol in the above problem
We will see a rectangle with width of 6.4 Feet and length of 8 Feet(height of the box) we need to find the diagnol again of this rectangle as we did in the above problem
so the diagnol will be sqrt(8^2 + (6.4)^2)
= Sqrt(64 + 41)
= Sqrt(101)= 10.04 Feet