Question

three pieces of timber 42 m 49 m and 63 m long have to be divided into the planks of the same 
length. what is the greatest possible length of each plank?

Answer 1

there are 3 separate pieces of timber - they cannot be joined together to make planks.  We need to make many planks of equal length.  We do not want to waste any timber.

It we cut 42 m long timber from all the three pieces,  then there is no waste from the 1st one, there is a waste of 7m from 2nd timber and 21 m length is wasted from the third .    We get  3 planks of 42 m length.
 
If we take HCF of all the given lengths (42, 49, 63) , it is 7 m.  Hence we make planks of length 7m, then we get 6+7+9 = 22 planks of equal length 7 m.

Answer 2

Answer:

The greatest possible length of each plank = 7 meter

Step-by-step explanation:

Length of the three pieces of the timber are given to be : 42 meter , 49 meter and 63 meter

Now, Given that these given pieces of timber are divided into the planks of the same length.

We need to find the greatest possible length of each plank.

So, to find the greatest possible length of each plank we need to find the H.C.F. of the given lengths of the pieces of timber

⇒ H.C.F. of (42 , 49 , 63)

42 = 2 × 3 × 7

49 = 7 × 7

63 = 3 × 3 × 7

So, The H.C.F. is 7

Hence, The greatest possible length of each plank = 7 meter