Question

Solution
Question
The length, breadth and height of a room are 252 cm,
144 cm and 72 cm respectively. Find the longest tape
which can measure the three dimensions of the room
exactly.
DOD CHART​

Answer 1

Given :

• Length of the room = 252 cm

• Breadth of the room = 144 cm

• Height of the room = 72 cm

To Find :

• The longest tape which can measure the three dimensions exactly

Solution :

In order to find the longest tape we have to find the HCF of the given length,breadth and height

→ HCF of 252 = 2 × 2 × 3 × 3 × 7

→ HCF of 144 = 2 × 2 × 2 × 2 × 3 × 3

→ HCF of 72 = 2 × 2 × 2 × 3 × 3

Common Factors : 2, 2, 3 and 3

So HCF = 2 × 2 × 3 × 3

→ HCF = 36

$\therefore$ Longest Measuring Tape = 36 cm

Answer 2

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.

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

Noa finding HCF of 252,144 & 72:-

$\sf Now, \\\sf 252 = 2 \times 126 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 63 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 21\\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 3 \times 7$

$\rule{100}{2}$

$\sf Again,\\\sf 144 = 2 \times 72 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 36 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 18\\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 2 \times 9 \\\\\sf \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 2 \times 3 \times 3$

$\rule{100}{2}$

$\sf And\: again, \\\sf 72 = 2 \times 36 \\\\\sf \: \: \: \: \: \: \: = 2 \times 2 \times 18 \\\\\sf \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 9 \\\\\sf \: \: \: \: \: \: = 2 \times 2 \times 2 \times 3 \times 3$

Now,common factors = 2 × 2 × 3 ×3

$\therefore$ HCF = 36

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