Question

The length and breadth of a room are 6 m 30 cm and 5 m 85 cm. Find the largest rod which can measure the two dimensions of the room exactly. (ਇੱਕ ਕਮਰੇ ਦੀ ਲੰਬਾਈ ਅਤੇ ਚੌੜਾਈ 6 ਮੀਟਰ 30 ਸੈਂਟੀਮੀਟਰ ਅਤੇ 5 ਮੀਟਰ 85 ਸੈਂਟੀਮੀਟਰ ਹੈ। ਸਭ ਤੋਂ ਵੱਡੀ ਸੋਟੀ ਦਾ ਮਾਪ ਲੱਭੋ ਜੋ ਕਮਰੇ ਦੇ ਦੋਵਾਂ ਮਾਪਾਂ ਨੂੰ ਬਿਲਕੁਲ ਮਾਪ ਸਕਦਾ ਹੈ।) * 45 cm 36 cm 25 cm 65 cm Q 27. ਦਿੱਤੇ ਚਿੱਤਰ ਵਿੱਚ, PQ || RS ਹੈ, ਤਾਂ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Length of the room = 6 m 30 cm = 630 cm

Breadth of the room = 5 m 85 cm = 585 cm

Now, we have to find the largest rod which can measure the two dimensions of the room exactly.

It means, we have to find that largest number which exactly divides 630 and 585.

It means, we have to find HCF of 630 and 585.

So, we have to first find prime factorization of 630 and 585.

$\red{\bf :\longmapsto\:Prime \: factorization \: of \: 630}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:630 \:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:315 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:105\:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:35 \:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:7\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\red{\sf :\longmapsto\:Prime \: factorization \: of \: 630 = 2 \times {3}^{2} \times 5 \times 7 }$

$\blue{\bf :\longmapsto\:Prime \: factorization \: of \: 585}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{5}}}&{\underline{\sf{\:\:585 \:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:117 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:39\:\:}} \\ {\underline{\sf{13}}}& \underline{\sf{\:\:13 \:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\blue{\sf :\longmapsto\:Prime \: factorization \: of \: 585 = {3}^{2} \times 5 \times 13}$

Now, we have

$\red{\sf :\longmapsto\:Prime \: factorization \: of \: 630 = 2 \times {3}^{2} \times 5 \times 7 }$

$\blue{\sf :\longmapsto\:Prime \: factorization \: of \: 585 = {3}^{2} \times 5 \times 13}$

Hence,

$\rm :\longmapsto\:HCF ( 585, 630 ) = {3}^{2} \times 5 = 9 \times 5 = 45$

Hence,

The length of longest rod that measures exactly 585 cm and 630 cm is 45 cm or 0.45 m.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The length and breadth of a room are 6 m 30 cm and 5 m 85 cm. Find the largest rod which can measure the two dimensions of the room exactly.

45 cm

36 cm

25 cm

65 cm

EVALUATION

Here it is given that the length and breadth of a room are 6 m 30 cm and 5 m 85 cm

Now 6 m 30 cm = 630 cm

5 m 85 cm = 585 cm

Now we have to find the the largest rod which can measure the two dimensions of the room exactly.

Now the required length

= HCF of the given lengths 630 cm , 585 cm

We now prime factorise the given numbers

$\sf{630}$

$\sf{ = 2 \times 3 \times 3 \times 5 \times 7}$

$\sf{ = 2 \times {3}^{2} \times 5 \times 7}$

$\sf{585 }$

$\sf{ = 3 \times 3 \times 5 \times 13}$

So HCF of 630 and 585

= 3 × 3 × 5

= 45

Hence the required length = 45 cm

The largest rod which can measure the two dimensions of the room exactly = 45 cm

FINAL ANSWER

Hence the correct option is 45 cm

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If the HCF of 20 and 35 is 5, LCM of 20 and 35 is 70 X a, then the value of a is

https://brainly.in/question/21460926

2. If HCF of two numbers be 40 then which of the following cannot be their LCM.

https://brainly.in/question/28609013