Question

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively,
Find the longest tape which can measure the three dimensions of the room exactly.
actly divisible by 6.8 and 12.​

Answer 1

We need to find H.C.F of 825, 675 and 450 which would be equal to the longest tape which can measure the three dimensions of the room exactly.

 

Let's find the prime factors of 825, 675 and 450.

 

825=3×5×5×11

 

675=3×3×3×5×5

 

450=2×3×3×5×5

 

 

3, 5 and 5 are the common prime factors.

 

Therefore. H.C.F =3×5×5=75

Therefore, 75 cm is the longest tape which can measure the three dimensions of the room exactly.

Answer 2

$length = 825cm = 3 \times 5 \times 5 \times 11$

$breadth = 675cm = 3 \times 3 \times 3 \times 5 \times 5$

$height = 450cm = 2 \times 3 \times 3 \times 5 \times 5$

$longest \: \: tape = hcf \: of \: 825 \: \: 675 \: \: and \:$

$450 = 3 \times 5 \times 5 = 75$

$longest \: \: tape \: is \: 75cm$

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