Question

the Length breadth and height of a room and 144 CM 120 CM 180 cm respectively the maximum length of an instrument which can be measure all the dimension is​

Answer 1

Answer:

Length of the longest tape = 36 cm

Step-by-step explanation:-

✏ Given:-

◗ Length = 252 cm

◗ Breadth = 144 cm

◗ Height = 72 cm

✏ To find:-

◗ Length of longest tape which can measure the dimensions of room = ?

✏ Solution:-

As the given dimensions are 252 cm,144 cm & 72 cm.And the tape needed to measure them is the longest tape.

As we know that to find the longest tape,we need to find the HCF.

\sf\green{[\because HCF = Highest \: common \: factor]}[∵HCF=Highestcommonfactor]

Noa finding HCF of 252,144 & 72:-

\begin{gathered}\sf Now, \\\sf 252 = 2 \times 126 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 63 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 21\\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 3 \times 7\end{gathered}

Now,

252=2×126

=2×2×63

=2×2×3×21

=2×2×3×3×7

\rule{100}{2}

\begin{gathered}\sf Again,\\\sf 144 = 2 \times 72 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 36 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 18\\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 2 \times 9 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 2 \times 3 \times 3\end{gathered}

Again,

144=2×72

=2×2×36

=2×2×2×18

=2×2×2×2×9

=2×2×2×2×3×3

\rule{100}{2}

\begin{gathered}\sf And\: again, \\\sf 72 = 2 \times 36 \\\\\sf \: \: \: \: \: \: \: = 2 \times 2 \times 18 \\\\\sf \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 9 \\\\\sf \: \: \: \: \: \: = 2 \times 2 \times 2 \times 3 \times 3\end{gathered}

Andagain,

72=2×36

=2×2×18

=2×2×2×9

=2×2×2×3×3

Now,common factors = 2 × 2 × 3 ×3

\therefore∴ HCF = 36

\therefore{\underline{\textsf{Length \: of \: longest \: tape = {\textbf{36 \: cm }}}}}∴

Length of longest tape = 36 cm

Step-by-step explanation:

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