Question

Hola Mates ♥♥

Plzz help me !!
.
. The length, breadth and height of a room are 8m 50 cm, 6m 25 cm and 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.



CLASS - X
MATHS
CH- REAL NUMBERS

Answer 1

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Here firstly, we convert the given dimensions into cm
So,
=) 8m 50 cm = 825 cm

=) 6m 25cm = 675 cm

=) 4m 75cm = 450 cm

Now, H.C.F of 825, 675 and 450

Using prime factorization method we get :-

● 825 = 3×5^2×11

● 675 = 3^3×5^2

● 450 = 2×3^2×5^2

Therefore,
HCF= 3× 5^2=75

Hence, the longest rod which can measure the three dimensions of the room exactly will be 75 cm long.


Hope it helps

Answer 2

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

Dear ,

Your Answer is ; 75 cm.

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• Step by Step Explanation ;-
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Given that ;-
• Length of the room = 8.25 m or 825 cm
• Breadth of the room = 6.75 m = 675 cm
• Height of the room = 4.50 m = 450 cm

Now ,
We have to find the longest rod that can measure the three dimensions of the room exactly. For this, we have to find the Highest Common Factor of 825, 675 and 450.

So ,
Prime factorization of 825 = 3*5*5*11
Prime factorization of 675 = 3*3*3*5*5
Prime factorization = 450 = 2*3*3*5*5

Now ,
Common factors = 3*5*5

H.C.F. = 75

Therefore
H.C.F. of 825, 675 and 450 is 75

• The length of the longest rod is 75 cm which can measure the three dimensions of the room exactly.

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