Question

The length, breadth and height of a room are 363m, 528m and 693m

respectively. Determine the longest tape that can measure the three dimensions of

the room exactly.​

Answer 1

The length of the longest tape that can measure the three dimensions of the room exactly is 33 meters.

GIVEN

The length, breadth and height of a room are 363m, 528m and 693m respectively.

TO FIND

Length of the longest tape that can measure the three dimensions of the room exactly.

SOLUTION

We can simply solve the above problem as follows;

The length of the longest tape will be equal to the HCF of the dimensions of the room.

Therefore,

HCF of 363, 528, 693 by prime factorisation is as follows;

363 = 3 × 11 × 11

528 = 2×2×2×2 × 3× 11

693 = 3× 3×7×11

HCF = 11× 3 = 33 m

Hence, The length of the longest tape that can measure the three dimensions of the room exactly is 33 meters.

#Spj2

Answer 2

Answer:

The answer to the given question is The length of the longest tape is 33 meters.

Step-by-step explanation:

Given :

The length, breadth and height of a room are 363m, 528m and 693m

To find :

The longest tape's length measures the three dimensions of the room exactly.

Solution :

The problem can be solved by determining the HCF of the dimensions because the length of the longest tape will be equal to the HCF of the dimensions of the room.

The HCF can be found by the prime factorization method.

let's do the prime factorization for these three dimensions.

The prime factorization of 363 will be

$3)363 \\ 11)121 \\ )11$

The prime factorisation of 528 will be

$2)528 \\ 2)264 \\ 2)132 \\2 )66 \\ 3)33 \\ )11$

The prime factorisation of 693 will be.

$3)693 \\ 3)231 \\ 7)77 \\ )11$

The factors of the numbers will be

$363 = 3 \times 11 \times 11 \\ 528 = 2 \times 2 \times 2 \times 2 \times 3 \times 11 \\ 693 = 3 \times 3 \times 7 \times 11$

The common value in each of the number is 3 and 11.

Therefore, the HCF of the numbers 363,693 and 528 will be 3 and 11

Hence, the length of the longest tape is

$3 \times 11 = 33$

33 meters is the final answer.

# spj6

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