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Measurements of a room are
7m50cm,6m&
3m75cm. Find the length of the longest rod that can measure all the three dimensions of the room.

Measurements of a room are $7\mathrm{~m} 50 \mathrm{~cm}, 6 \mathrm{~m} \&$ $3 \mathrm{~m} 75 \mathrm{~cm}$ . 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\mathrm{~m} 50 \mathrm{~cm}, 6 \mathrm{~m} \&

3 \mathrm{~m} 75 \mathrm{~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. $\newline$ $7\text{m} 50\text{cm} = 750\text{cm}$ , $6\text{m} = 600\text{cm}$ , $3\text{m} 75\text{cm} = 375\text{cm}$ .
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 $750$ , $600$ , and $375$ . $\newline$ Using prime factorization: $\newline$ $750 = 2 \times 3 \times 5^3$ $\newline$ $600 = 2^2 \times 3 \times 5^2$ $\newline$ $375 = 3 \times 5^3$ $\newline$ Common factors are $3$ and $5^2$ . $\newline$ GCD = $3 \times 5^2 = 75\,\text{cm}$ .

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