Question

296 29. Three pieces of timber, 42-m, 49-m and 63-m long, have to be divided into planks of the 799 481 same length. What is the greatest possible length of each plank?
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Answer 1

Answer:

➡️Given:

• 42m, 49m and 63 m long.
• to divide into planks of the 799 481 .

➡️To find:

• Greatest possible length of each plank is?

➡️Solution:

Length of three pieces are given respectively ,

We have to divide the timber into equal length of planks.

$\sf \red{HCF \: of \: (42,49,63)}$

$\sf \red\hookrightarrow \red{HCF \: is \: 7}$

$\sf \red \bigstar{Another \: method \: is} :$

Prime factorization:

$\sf{42 = 2 \times 3 \times 7}$

$\sf{49 = 7 \times 7}$

$\sf{63 = 3 \times 3 \times 7}$

Hence,

The greatest possible length of each plank is

$\huge \boxed { \frak \leadsto\pink{7m}}$

Answer 2

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: question\::-}}}}}$

Three pieces of timber, 42-m, 49-m and 63-m long, have to be divided into planks of the 799 481 same length. What is the greatest possible length of each plank?

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: given\::-}}}}}$

Three pieces of timber, 42-m, 49-m and 63-m long, have to be divided into planks of the 799 481 same length..

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: to \: find\::-}}}}}$

the greatest possible length of each plank

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: solution\::-}}}}}$

we need to find the greatest possible length of each plank

so therefore, to find the greatest possible length of each plank we need to find the h.c.f of the given pieces and timber

now according to question

$\sf⇝ h.c.f \: of \: (42 \: 49 \: 63) \: are \:$

$\sf⇝42 = 2 \times 3 \times 7$

$\sf⇝63 = 3 \times 3 \times 7$

$\sf⇝so \: the \: hcf \: is \: 7$

so therefore the greatest possible length of each plank is 7