The measurement of a room are 7m 50cm, 6m and 3m 75cm. Find the length of the longest rod that can measure all the three dimensions of the room exactly.
Answers
If the measurement of a room are 7m 50cm, 6m and 3m 75cm then the length of the longest rod that can measure all the three dimensions of the room exactly is 0.75 m or 75 cm.
Step-by-step explanation:
The length of the room = 7m 50 cm = 7 + 0.5 = 7.5 m
The breadth of the room = 6 m
The height of the room = 3 m 75 cm = 3 + 0.75 = 3.75 m
Now, in order to find the length of the longest rod that can measure all the three dimensions of the room exactly we will find the H.C.F of the 7.5, 6 & 3.75 by long division method:
3.75 ) 6 ( 1
3.75
-----------------
2.25 ) 3.75 ( 1
2.75
-------------
1.5 ) 2.25 ( 1
1.5
--------------------
0.75) 1.5 ( 2
1.5
--------------------
X
---------------------
So, the H.C.F of 3.75 m and 6 m is 0.75 m.
0.75 ) 7.5 ( 9
6.75
-----------------
0.75 ) 0.75 ( 1
0.75
-------------
x
-----------------
So, the H.C.F of 0.75 m & 7.5 m is 0.75 m
∴ H.C.F of 3.75 m, 6 m and 7.5 m is 0.75 m or 75 cm
Thus, the length of the longest rod that can measure all the three dimensions of the room exactly is 0.75 m or 75 cm.
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Length of the room = 7m 50cm = 750cm
Breadth of the room = 6m = 600cm
Height of the room = 3m 75cm = 375cm
Prime factorization of 750, 600 and 375 are as follows:
750 = 2×3×5×5×5
600 = 2×2×2×3×5×5
375 = 3×5×5×5
HCF = 3×5×5
HCF = 3×5×5 = 75
Therefore the length of the longest tap is 75 cm which can measure the three dimensions of the room exactly.