The length, breadth and height of a tank are 220
cm, 84 cm and 60 cm respectively. Determine the
longest rod which can measure the three
dimensions of the tank exactly.
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Asked on May 01, 2020 byBablu Jeet
The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
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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: 4cm
Step-by-step explanation:
We need to find H.C.F of 220, 84 and 60 which would be equal to the longest tape which can measure the three dimensions of the room exactly.
Let's find the prime factors of 220, 84 and 60.
Length = 220 cm = 2 x 2 x 5 x 11
Breadth = 84 cm = 2 × 2 × 3 × 7
Height = 60 cm = 2 × 2 × 3 × 5
Longest tape = HCF of 220, 84, and 60 = 2 x 2= 4 cm
Therefore, 4 cm is the longest tape which can measure the three dimensions of the room exactly.