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Question
The length, breadth and height of a room are 8m25cm,6m75cm and 4m50cm respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.
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Solution
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
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.
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 = 75
Therefore, the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm
Length = 825 cm
Breadth = 675 cm
Height = 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.
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 = 75
Therefore, the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm
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