Question

the Length breadth and height of a room are 8m 20 CM 6M 75 cm and 4m 50 cm respectively determine the longest rod which can measure the three dimension of the root exact

Answer 1

Length of the room, l = 8 m 20 cm = ( 8 * 100 ) + 20 cm = 820 cm

Breadth of the room, b = 6 m 75 cm = ( 6 * 100 ) + 75 cm = 675 cm

Height of the room, h = 4 m 50 cm = ( 4 * 100 ) + 50 cm = 450 cm

We know that in a solid figure, the longest rod that can be exactly fit in it is its diagonal.

Also, diagonal of a cuboid is the square of the sum of the squares of its length, its breadth and its height.

Diagonal of the cuboidal room, D = $\bold{\sqrt{l^2 + b^2 + c^2} ~~cm}$

D = $\bold{\sqrt{820^2 + 675^2 + 450^2} ~~cm}$

D = $\bold{\sqrt{672400 + 455625 + 202500} ~~cm}$

D = $\bold{\sqrt{1330525} ~~cm}$

D = $\bold{1153.48385338~~cm}$

On rounding off,

D = $\bold{1153.48~~cm}$

Hence,

A rod $\bold{1153.48385338~~cm}$ long can measure the three - dimensional figure i.e. the room exactly.

Answer 2

Here is your solution

Given :-

A room with

Length = 8m 20 cm = 820cm

Breadth = 6M 75 cm = 675cm

Height = 4m 50 cm = 450cm

To find Longest rode:-

As we know that diagonals is the longest rode .

We know the formula of diagonals of cuboid.

$D = \sqrt{l {}^{2} + b {}^{2} + h {}^{2} } \\ D= \sqrt{820 {}^{2} + 675 {}^{2} + 450 {}^{2} } \\ D = \sqrt{672400 + 455625 + 202500} \\ D = \sqrt{1330525} \\ D = 1153.48385338cm\\ D = 1153.48cm(round \: off \: of \: 11.5348385338)$

Hence,
The longest rode is 1153.48cm

Hope it helps you