the edges of a rectangular box are 3, 4, and 5 inches. What is the maximal distance between pairs of corners?

Answer 1

the max distance in a rectangular solid is its diagonal,, like in a rectangle, the max distance is the diagonal,,
recall: the square of the diagonal of a rectangular solid the sum of the squares of its sides, or:
L^2 + W^2 + H^2 = D^2
where
L=length, W=width, H=height, D=diagonal
or taking the squareroot:
D = sqrt(L^2 + W^2 + H^2)
substituting the values:
D = sqrt(5^2 + 4^2 + 3^2)
D = 5*sqrt(2) = 7.07 inches

hope this helps~ :)