Question

The length, breadthand height of a room are
8m 25cm, 6m 75 cm and
4m 50 cm respectively​

Answer 1

Answer:

Length of the room = 8m 25cm = 825 cm

Breadth of the room = 6m 75cm = 675 cm

Height of the room = 4m 50cm = 450 cm

Prime factorization of 825, 675 and 450 are as follows:

825 = 3×5×5×11

675 = 3×3×3×5×5

450 = 2×3×3×5×5

 

Common factors = 3×5×5

H.C.F. = 75

 Hence, H.C.F. of 825, 675 and 450 is 75.

Therefore the length of the longest tap is 75 cm which can measure the three dimensions of the room exactly.

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Answer 2

Answer:

Step-by-step explanation:

The dimensions are 825 cm, 675 cm and 450 cm.

For any rod to be capable of measuring a side, the length of the side must be a multiple of the length of the rod.

Hence, we need a rod of length (in cm) which is a factor of 825 , 675 and 450.  

For the rod to be of highest possible length we need to find the HCF of 825 , 675 and 450.  

Using prime factorization:

825 = 3×52×11

675 = 33×52

450 = 2×32×52

From the above, HCF = 3×52 = 75

Hence, the longest rod which can measure the three dimensions of the room exactly will be 75 cm long.