Here is a box with a length of 12 cm and a height of 8 cm and a width of 9 cm.

Find the length of a line that goes from the left bottom corner to the right top corner.

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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)`

= `17`

**Therefore, the length of a line that goes from the left bottom corner to the right top corner of the box is 17 cm.**

**Sources:**

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