Given that the sides of a box are 6 X 8 X 24 cm.
Then, we know that the longest part of the box is the diagonal.
Then we need to calculate the diagonal.
The diagonal is:
D = sqrt( a^2 + b^2 + c^2 ) where a , b, and, c are the sides of the box:
==> D = sqrt( 6^2 + 8^2 + 24^2)
==> D = sqrt( 36 + 64 + 576)
==? D = sqrt( 676)
==> D = 26
Then, the longest stick that we can fit in the box is 26 cm .
We are given a rectangular box with the dimensions 6 cm, 8 cm and 24 cm. We have to find the length of the longest stick that can be placed in the box.
This length is equal to the diagonal of the box. We can calculate the length of the diagonal of a rectangular box of sides A, B and C by the expression sqrt (A^2 + B^2 + C^2). Here this is equal to sqrt (6^2 + 8^2 + 24^2).
sqrt (6^2 + 8^2 + 24^2) = sqrt (36 + 64 + 576) = sqrt (676) = 26 cm.
The required length of the longest stick is 26 cm.
The longest stick that could be placed in the rectangular box of dimension 6cm , 8cm and 24cm is the diagonal of the box.
To find the diagonal of the box, first we find the bottom surface diagonal:
We imagine that the box has the bottom surface with length 8cm and width 6cm.
Therefore the diagonal d of the bottom surface is given by:
d^2 = 6^2+8^2 = 100.
The height h of the box : h = 24.
Therefore the diagonal D of the box is the line from one corner of the bottom surface to to the opposite corner on the top surface.
The diagonal D of the the box is got by:
D^2 = d^2+h^2, where h = heght of the bos which is 24.
Therefore D^2 = d^2+h^2 = 100 +24^2 = 100 + 576 = 676.
Therefore D = sqrt(676) = 26.
So the longest stick that could be placed in the box = 26cm.