Question

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

Answer 1

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, $\angle$B = 90° we can see that AC is the hypotenuse if we consider

$\Delta$ ABC, $A{C}^2=B{C}^2+A{B}^2$
$\Rightarrow$ $A{C}^2={12}^2+9^2$
$\Rightarrow$ $A{C}^2=144+81$
$\Rightarrow$ $AC=(\sqrt{225}$)
$\Rightarrow$ 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 $\Delta$ ACE is another right $\Delta$ where $\angle$C = 90°. Using Pythagoras theorem again, we have AE = 17 m.