Question

Mr. Shayam has recently shifted in his new house. When he entered in master bed room and observed uts dimensions 8m × 6m × 4m. He decided to put one longest rod into it. The length of the longest rod will be

Answer 1

Answer:

10 m

Step-by-step explanation:

As the dimensions of 8m and 6 m are greater one, so

the length of diagonal = sqrt(8^2 + 6^2)

                                     = 10 m

Answer 2

Given:

Mr Shayam has recently shifted to his new house. When he entered the master bedroom and observed its dimensions 8m × 6m × 4m. He decided to put one longest rod into it

To Find:

The length of the longest rod will be

Solution:

The longest rod as many of us think that will be the diagonal of the plane with dimension 8*6 that is the floor of the room but it is not the longest we can fit a longer one in the room that is the diagonal of the cuboid (room) that is the length from one upper corner to directly opposite down corner( i am attaching a diagram for you to visualize the situation)

first, we will need to calculate the diagonal of the floor that will be,

$D=\sqrt{8^2+6^2} \\=\sqrt{64+36}\\=10m$

Now takins diagonal and the height of the room we will find the diagonal of the room, moving further we get,

$D=\sqrt{10^2+4^2}\\=\sqrt{100+16}\\ =\sqrt{116}\\=2\sqrt{29}\\=10.77m$

Hence, the length of the longest rod that can be fitted in a room of dimensions 8*6*4 is 10.77m.