Question

The length of two rods are 6m 75cm and 15m 50cm.Find the length of the longest tape which can measure these length exactly.
please help me out I need this no. 5question ans explain​

Answer 1

In the above Question the following information is given -

The length of two rods are 6m 75cm and 15m 50cm respectively .

Find the length of the longest tape which can measure these lengths .

Solution -

Here , these two rods measure 6m 75cm and 15m 50cm respectively .

Now ,

The length of the longest tape which can measure these lengths , can be found out by taking the HCF of the two rod lengths .

Rod 1 => 675 cm

Rod 2 => 1550 cm

675 ) 1550 ( 2

1350

____

200 ) 675 ( 3

600

____

75 ) 200 ( 2

150

____

50 ) 75 ( 1

50

___

25 ) 50 ( 2

2

____

0

Hence , 25 cm is th required length of the tape that can measure .

This is the required answer .

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Answer 2

$\huge \boxed {\mathfrak {\orange { answer}}} \\\\ \sf Length_{1} \: = 6 \: m .\: 75 \: cm =675 \: cm \\ \sf Length_{2} = 15 \: m. \: 50 \: cm = 1550 \: cm \\\\\ \sf \red{The \: length \: of \: the \: longest \: tape} \\ \sf \red{=HCF \: of \: 675 \: and \: 1550} \\\\\sf HCF~of~ 675~ and~ 1550 \\ \sf by~ \green{Euclid's~Division ~Algorithm}:- \\\\ \sf 1550 = 675 \times 2 + 200 \\ \sf 675 = 200 \times 3 + 75 \\ \sf 200 = 75 \times 2 + 50 \\ \sf 75 = 50 \times 1 + 25 \\ \sf 50 = {\boxed{\sf { \pink{25}}}} \times 2 + 0 \\\\ \sf The \: HCF \: \: of \: 675 \: and \: 1550 = {\boxed{\sf { \green{25}}}} \\\\ \sf \purple{ \sf{The \: length \: of \: the \: longest \: tape \: is~}} \underline{\orange{ \sf{ 25 \: cm}}}.$