The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
Answers
SOLUTION :
Required length of the longest rod that can measure the dimensions of the exactly is equal to the HCF of 8m 25 cm , 6m 75m and 4m 50m. To find the HCF of all the dimensions, first of all we have to convert them in the same unit, then use any method for calculating HCF.
GIVEN :
Length of room = 8m 25 cm = 825 cm
[1 m = 100 cm]
Breadth of room = 6m 75m = 675 cm
Height of room = 4m 50 m = 450 cm
The length of the longest rod = HCF of 825, 675 and 450
First we take 675 and 450 to find the HCF , by applying Euclid’s division lemma(a = bq + r)
675 = 450 x 1 + 225
450 = 225 x 2 + 0
HCF of 675 and 450 = 825
Now , we take 625 and 825 to find the HCF , by applying Euclid’s division lemma(a = bq + r)
825 = 225 x 3 + 150
225 = 150 x 1+75
150 = 75 x 2 + 0
HCF of 825, 675 and 450 = 75
Hence, the required length of the longest rod is 75 cm.
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Correct Answer
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