Question
There is a room with dimensions 3 meter, 4 meter and 12 meter. What is the height of the longest pole that can be kept in the room ??
Answer
The longest pole that can fit in a rectangular room is that it stretches from one bottom corner to the opposite top corner.
This is known as space diagonal and it is a 2D version.
To solve the above problem, we must use 3D version of Pythagorean theorem.
The formula for space diagonal (d) of a box with length l, width w and height h is -----
d = sqrt ( l^2 + w^2 + h^2 )
Where l = 3m w = 4m h = 12m
==>> d = sqrt ( 3^2 + 4^2 + 12^2 )
==>> d = sqrt ( 9 + 16 + 144 )
==>> d = sqrt ( 169 )
==>> d = 13 m
The height of or length of longest pole that can be kept in the room is 13 m !!!
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