Question

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.
Find the longest tape which can measure the three dimensions of the room exactly​

Answer 1

AnswEr :

• The Length of room = 835 cm
• The Breadth of room = 675 cm
• The Height of room = 450 cm
• The Longest tape which can measure these given three dimensions of the room is.

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As we Have to Find the longest tape of three dimensions, therefore we will find the LCM of these three given dimensions.

★ LCM of the three Dimensions of the Room :

$\boxed{\begin{array}{r|l}3&825\\\cline{1-2}5&275\\\cline{1-2}5&55\\\cline{1-2}&11\end{array}}$ $\boxed{\begin{array}{r|l}3&675\\\cline{1-2}3&225\\\cline{1-2}3&75\\\cline{1-2}5&25\\\cline{1-2}&5\end{array}}$ $\boxed{\begin{array}{r|l}2&450\\\cline{1-2}3&225\\\cline{1-2}3&75\\\cline{1-2}5&25\\\cline{1-2}&5\end{array}}$

✇ Now, Let's find out the HCF From these dimensions (835 cm, 675 cm and 450 cm) —

↠ 825 = 3 × 5 × 5 × 11

↠ 675 = 3 × 3 × 3 × 5 × 5

↠ 450 = 2 × 3 × 5 × 3 × 5

Therefore,

• HCF of (825, 675 & 450) = 3 × 5 × 5 = 75.

∴ Hence, the longest tape which can easily measure the three dimensions of the room exactly should be 75 cm long.

Answer 2

Given :-

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.

To Find :-

Find the longest tape which can measure the three dimensions of the room exactly​

Solution :-

Finding the HCF of the dimensions

825 =  3 × 5 × 5 × 11  

675 = 3 × 3 × 3 × 5 × 5  

450 = 2 × 3 × 3 × 5 × 5

Now

Finding common factor

Common factors are = 3,5 and 5

3 × 5 × 5

15 × 5

75

75 is the HCF of 825, 675 and 450 cm. Therefore, 75 cm is the longest tape required