Question

the Length breadth and height of a room are 825cm, 675cm, and 450cm find the longest dimensions of the room exactly​

Answer 1

Solution:

Given:

=> Length of room = 825 cm

=> Breadth of room = 675 cm

=> Height of the room = 450 cm

To find:

=> Longest tape to measure dimensions of the room.

Formula used:

=> HCF

Now, we will find the HCF of all the dimensions of the room to calculate that longest tape.

HCF of 825:

$\begin{array}{r | l}3 & 825 \\\cline{2-2} 5 & 275 \\\cline{2-2} 5 & 55 \\\cline{2-2} 11 & 11 \\\cline{2-2} & 1\end{array}$

HCF of 675:

$\begin{array}{r | l}3 & 675 \\\cline{2-2} 3 & 225 \\\cline{2-2} 3 & 75 \\\cline{2-2} 5 & 25 \\\cline{2-2} 5 & 5 \\\cline{2-2} & 1\end{array}$

HCF of 450:

$\begin{array}{r | l}2 & 450 \\\cline{2-2} 3 & 225 \\\cline{2-2} 3 & 75 \\\cline{2-2} 5 & 25 \\\cline{2-2} 5 & 5 \\\cline{2-2} & 1\end{array}$

Therefore,

825 = 3 × 5 × 5 × 11

625 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

HCF of 825, 675 and 450 = 3 × 5 × 5 = 75 cm

Hence, longest tape = 75 cm.

Answer 2

$\huge✿ {\bold{ \pink{ᴬᴺˢᵂᴱᴿ:- }}}$

Given :

• Length of room = 825 cm
• Breadth of room = 675 cm
• Height of the room = 450 cm

Solution :

The Measurement of longest tape = H.C.F of 825 cm,675cm,and 450cm

Factor of 825 = 3 × 5 × 5 × 11

Factor of 675 = 3 × 5 × 5 × 3 × 3

Factor of 450 = 2 × 3 × 3 × 5 × 5

$\huge{H.C.F} \: = \small\pink{ 3 \: × \: 5 \: × \: 5 }$

$= \huge\red{75cm}$

Therefore, The Longest tape is 75 cm .