The dimensions of a room are 7m 20 cm, 5m 40 cm and 3m 60 cm. Find the longest stage which will measure these dimensions exactly
Answers
Answer:
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.
Hope this helps you☺
Step-by-step explanation:
let length of room = 7m 20 cm = 720 cm
and width of room = 5m 40 cm= 540 cm
height of room = 3m 60 cm = 360 cm
longest stage will be the HCF of these dimensions
by prime factorisation method,
720= 2×2×2×2×3×3×5
540= 2×2×3×3×3×5
360= 2×2×2×3×3×5
HCF = 2×2×3×3×5 = 180
Longest stage will measure 180 cm or 1m 80 cm.
hope it helps you
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