Question

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

Answer 1

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.

Answer 2

Answer:

given,

lenth= 8m 25cm= 8.25cm

breadth= 6m75cm=6.75m

hieght=4m 50cm= 4.5m

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

4.5)6.5(1

4.50

..................

2.25)4.5(2

4.5

.................

x