Question

find the length of the longest pole that can be placed in a room 12m long 8 metre broad and 9M high​

Answer 1

Given length l = 12 m

breadth b = 8m and height h = 9 m

Longest rod that can be placed in a room is nothing but its diagonal.

Length of diagonal of a cuboid = √(l²+b²+h²)

Length of longest rod = √(12² + 8²+9²) m

= √(144 + 64 + 81) m

= √289 m

= 17 m

Thus the length of the longest rod is 17 m

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Answer 2

Length of room=12 m
Breadth=8 m
Height=9m

Highest Pole can Placed in room is Equal to Diagonal of room.
Let Find Diagonal
$\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } \\ = \sqrt{ {12}^{2} + {8}^{2} + {9}^{2} } \\ = \sqrt{144 + 64 + 81} \\ = \sqrt{(8 + 9) {}^{2} } \\ = \sqrt{17} {}^{2} \\ = {17}^{2} {}^{ \frac{1}{2} } \\ = 17$
Now Understand
64+144+81
According to (a+b)²=a²+b²+2ab
√64=8
√81=9
So when we take on this identity
=(9+8)²=9²+8²+2×9×8
=(9+8)²=81+64+144

Now You Understand
Why We Multiply square
As √ means=^½
So we remove√and take^ 1/2
2 and 1/2 cut Remain 17
So Highest pole in room=17 m

$\boxed{\mathbf{Highest\:pole=17m}}$