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Measurements of a room are $7\text{m}50\text{cm}$ , $6\text{m}8$ $3\text{m}75\text{cm}$ . Find the length of the longest rod that can measure all the three dimensions of the room.

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Area and perimeter: word problems

Full solution

Q. Measurements of a room are

7\text{m}50\text{cm}

,

6\text{m}8

3\text{m}75\text{cm}

. Find the length of the longest rod that can measure all the three dimensions of the room.

Convert to centimeters: Convert all measurements to centimeters for uniformity. $7\text{m} 50\text{cm} = 750\text{cm}$ , $6\text{m} 8\text{cm} = 608\text{cm}$ , $3\text{m} 75\text{cm} = 375\text{cm}$ .
Find GCD for longest rod: Find the greatest common divisor (GCD) of the three measurements to determine the longest rod that can measure all dimensions. $\newline$ GCD of $750$ , $608$ , and $375$ . $\newline$ Using the Euclidean algorithm: $\newline$ $750$ and $608$ : $750 - 608 = 142$ $\newline$ $608$ and $142$ : $608 - 4\times142 = 48$ $\newline$ $142$ and $608$ $0$ : $608$ $1$ $\newline$ $608$ $0$ and $608$ $3$ : $608$ $4$ $\newline$ $608$ $3$ and $608$ $6$ : $608$ $7$ $\newline$ GCD is $608$ $6$ .

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