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Question

The length of the longest bar that can be fixed in a room of dimensions 12 m × 9 m × 8 m is ___ m.

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Solution

You can take a look at your own room for reference in this question. If you’re in a room right now, look at the wall that you’re facing, let the corners of this room be ABCD which is the face of a cuboid. The length of the cuboid is 12 m and the height is 9 m .Since, ABCD is a rectangle, B = 90° we can see that AC is the hypotenuse if we consider

Δ ABC, AC2=BC2+AB2
AC2=122+92
AC2=144+81
AC=(225)
AC = 15 m

We’ve been thinking in terms of 2 dimensional only till now but now let’s shift our focus to a little 3 dimensional thinking. Take a look at the figure given above, The Δ ACE is another right Δ where C = 90°. Using Pythagoras theorem again, we have AE = 17 m.


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