the measurements of a room are 7 m 50cm, 6 m and 3m 75cm.find length of longest rod that can measure all the three dimensions of the room exactly
Answers
Step-by-step explanation:
length of room = in cm is 750 cm
breadth of room = in cm is 600 cm
height of room = in cm is 375 cm
the tape required has to measure all three distance 750 cm ,600 cm ,375 cm in a way that the count is an exact number of times . so it's length must be an exact division of all three distance. moreover , this tape must be longest .
thus,the So,we find HCF of 750 cm , 600 cm , 375 cm
And there HCF will be,
750= 2×3×5×5×5
600= 2×2×2×5×5×3
375=5×5×5×3
common = 3×5×5=75
HCF = 75
hence HCF of 750,600,375 = 75 so, longest tape required is 75 cm
Hope , it will you it is long explanation but explained step by step
Answer:
Given :- Dimensions of Room =7.5mX6mX3.75m
The longest rod that can measure = Diagonal of Room
= \sqrt{l^{2} + b^{2} + h^{2} }=
l
2
+b
2
+h
2
= \sqrt{7.5 {}^{2} + 6 {}^{2} + 3.75 }=
7.5
2
+6
2
+3.75
= \sqrt{56.25 + 36 + 14.06}=
56.25+36+14.06
= \sqrt{106.31}=
106.31
= 10.31m=10.31m
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