A room is 12 metres long, 9 metres wide and 8 metres high. What is the longest rod that can be placed in it ?

Question

Accepted Answer

To determine the longest rod that can be placed in the room, we need to calculate the length of the room's diagonal. The room is a rectangular cuboid with dimensions 12 metres (length), 9 metres (width), and 8 metres (height). The formula to find the space diagonal $d$ of a cuboid is:

$$ d = \sqrt{l^2 + w^2 + h^2} $$

where $l$, $w$, and $h$ are the length, width, and height of the cuboid, respectively.

Substituting the given dimensions into the formula:

$$ d = \sqrt{12^2 + 9^2 + 8^2} $$
$$ d = \sqrt{144 + 81 + 64} $$
$$ d = \sqrt{289} $$
$$ d = 17 \text{ metres} $$

Therefore, the longest rod that can be placed in the room is 17 metres, which corresponds to Option 2.

**Explanation of why other options are incorrect:**

1. **Option 1 (29 metres):** This option is incorrect because the calculated diagonal of the room is 17 metres. A rod of 29 metres would exceed the maximum possible diagonal length of the room.

2. **Option 3 (15 metres):** This option is incorrect because it is less than the calculated diagonal of 17 metres. While a 15-metre rod could fit within the room, it is not the longest possible rod that can be placed diagonally.

3. **Option 4 (21 metres):** This option is incorrect because it exceeds the calculated diagonal of 17 metres. A rod of 21 metres would not fit within the room's dimensions.

In conclusion, based on the calculation of the room's diagonal, Option 2 (17 metres) is the correct answer for the longest rod that can be placed in the room.