Question

the Length breadth and height of a room are 8 metre 25 CM 6 CM 75 cm and 4m 50 CM, respectively determine the longest rod which can measure the three dimensions of the room exactly

Answer 1

Given,

Length = 8 m 25 cm = 8.25 m

Breadth = 6 m 75 cm = 6.75 m

Height = 4 m 50 cm = 4.5 m.

The longest rod that can measure all 3 dimensions of room exactly is their H.C.F.

      4.5 ) 6.75 ( 1
           
              4.50

       -----------------
             2.25 ) 4.5 ( 2

                        4.5
                  -------------
                         x

So, H.C.F of 4.5 m and 6.75 m is 2.25 m.

Now ,

       2.25 ) 8.25 ( 3

                 6.75
           --------------
                 1.5 ) 2.25 ( 1
             
                          1.5
                      ------------
                         0.75 ) 1.5 ( 2

                                   1.5
                               -------------
                                     x

So, the H.C.F of 8.25 m , 6.75 m and 4.5 m is 0.75 m.

Hence , answer is 0.75 m ( 75 cm ).
        

Answer 2

hey friend!!!

your answer is "75cm"

Explaination
____

Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively.

Length = 825 cm
Breadth = 675 cm
Height = 450 cm

HCF of 825, 675, 450

825 = 5 x 5 x 3 x 11
675 = 5 x 5 x 3 x 3 x 3
450 = 2 x 3 x 3 x 5 x 5

HCF = 5 x 5 x 3 = 75cm_____answer

Therefore, the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm

I think my answer is capable to clear your confusion..