Question

The length, breadth and height of a box are respectively 12 dm, 4 dm and 3 dm. Find the length of the greatest rod that can be put in it.


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Answer 1

See the attached image

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Answer 2

given that Length l= 12 dm

breadth b=4 dm

height h=3 dm

Longest rod that can be placed in a room is nothing but its diagonal.

Length of diagonal of a cuboid

$\sqrt{(l { }^{2} } + b {}^{2} + h {}^{2})dm$

length of longest rod=

$\sqrt{(12 {}^{2} }+4{}^{2}+3{}^{2}) = \sqrt{169 }dm = 13dm$

The length of the longest rod is 13 dm