Question

5) The length of longest rod that can be placed in a room of dimensions 12mx9mx8m
a) 21m
b) 20 m
c) 17 m
d) 15 m
​

Answer 1

$\sf{\huge{\underline{\pink{Given :-}}}}$

• A room of dimensions 12mx9mx8m.

$\sf{\huge{\underline{\red{To\:Find :-}}}}$

• The length of longest rod that can be placed in that room.

$\sf{\huge{\underline{\orange{Answer :-}}}}$

According to the question,

The dimensions of the room are 12mx9mx8m .

• Length = 12 m

• Breadth = 9 m

• Height = 8 m

Clearly, We find out that it's a rectangular room.

So if we put rod diagonally that's the longest length rod which fit inside the given room .

Hence, the length of the rod = The length of diagonal of the rectangle

We know that, the diagonal of a rectangle =

$\sqrt{{l}^{2} + {b}^{2} + {h}^{2} }$

Putting Values,

➝ $\sqrt{{12}^{2} + {9}^{2} + {8}^{2} }$

➝ $\sqrt{{144} + {81} + {64} }$

➝ $\sqrt{289 }$

➝ 17 meters

Hence,The length of longest rod that can be placed in that room is 17 meters .