Question

The length, breadth and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the
length of the longest rod that can measure the dimensions of the room exactly.​

Answer 1

$\huge\fcolorbox{black}{aqua}{Solution:-}$

✏️ Answer:-

★ The length of the longest rod that can measure the dimensions of the room exactly is 25 cm.

✏️ Step-by-step explanation:-

★ Given :-

• Length, l = 8m 50cm i.e., 850 cm;

• Width, w = 6m 25cm = 625 cm;

• Height, h = 4m 75cm = 475 cm.

★ To find :-

• The length of the longest rod that can measure the dimensions of the room.

★ Rationale :-

∵ The length of the longest rod is equal to the HCF of 850, 625 and 475,

Thus, by using the method of prime factorisation, we get,

• 850 = 2 x 5 x 5 x 17

⇒The factors of 850 are 1, 2, 5, 17, 10, 25, 34, 50, 85, 170, 425 and 850.

• 625 = 5 x 5 x 5 x 5

⇒The factors of 625 are 1, 5, 25, 125 and 625.

• 475 = 5 x 5 x 19

⇒The factors of 475 are 1, 5, 19, 25, 95 and 475.

Now,

From the above scenario,

We can conclude that,

HCF (850, 625, 475) = 25 .

∴ The longest rod that can measure the dimensions of the room exactly is 25 cm.

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❐ Commonly Made Errors —

• Most candidates are unable to determine 'bout what they have to find. They seem to find it difficult to make out if the question is 'bout HCF or LCM.

• Sometimes students calculate the longest length of rod that lies in the room by finding its diagonal.

❐ Answering Tips —

• Adequate practice is necessary for such type of questions and basic concepts of HCF and LCM must be clear.

• Students are ought to read the question properly before attempting it.

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I hope this helps! :)