The length, breadth and height of a room are 825, 675 and 450cm respectively. Find the longest tape which can measure the three dimesions of the room exactly.
a.70 cm
b.75 cm
c.80 cm
d. 85 cm
a.70 cm
b.75 cm
c.80 cm
d. 85 cm
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Answer:
The longest tape that can measure the three dimensions of the room exactly can be found by finding the highest common factor (HCF) of the three dimensions.
HCF of 825, 675, and 450 can be calculated using the prime factorization method:
825 = 3 * 5^2 * 11
675 = 3^3 * 5^2
450 = 2 * 3^2 * 5^2
The common factors are 3 * 5^2 = 75.
Therefore, the longest tape that can measure the three dimensions of the room exactly is 75 cm.
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