The given box is of cuboidal shape, with length = 12 cm, breadth = 9 cm and height = 8 cm.
The length of the line that goes from the left bottom corner to the right top corner of the box is its longest diagonal or body diagonal. If l, b and h denote the length, breadth and height of a cuboid, and d is the body diagonal (the longest diagonal), then
`d = sqrt (l^2 + b^2 + h^2)`
Here, `d = sqrt (12^2 + 9^2 + 8^2) `
= `sqrt (144 + 81 + 64)`
= `sqrt (289)`
Therefore, the length of a line that goes from the left bottom corner to the right top corner of the box is 17 cm.