Question

The length, breadth and height of a room are 725 cm, 925 cm and 825 cm respectively. Determine the length of the largest tape which can measure the three dimensions of the room exactly.


​

Answer 1

Given :

• Length of the room = 725 cm.

• Breadth of the room = 925 cm.

• Height of the room = 825 cm.

To find :

• The length of the largest tape which can measure the three dimensions of the room exactly =?

Step-by-step explanation :

Length of the room = 725 cm.

Breadth of the room = 925 cm.

Height of the room = 825 cm.

We have to find the length of the largest tape which can measure the three dimensions of the room exactly. So, HCF ( Highest Common Factor) of the given dimensions.

HCF of 725, 925 and 825 :-

➮ 725 = 5 × 5 × 29

➮ 925 = 5 × 5 × 37

➮ 825 = 3 × 5 × 5 × 11

•°• HCF = 5 × 5 = 25

Therefore, the length of the largest tape which can measure the three dimensions of the room exactly = 25 cm.

Answer 2

$\rule{200}3$

Given :-

• Length of the room = 725 cm.

• Breadth of the room = 925 cm.

• Height of the room = 825 cm.

$\rule{200}3$

To find :-

Largest tape to measure length, Breadth and height.

$\rule{200}3$

Step by step Explaination :-

$\therefore$ largest measuring tape = HCF of 725, 925, 825

HCF of 725, 925, 825

$\begin{array}{r | l}</p><p></p><p>5 & 725 \\</p><p></p><p>\cline{2-2} 5 & 145 \\</p><p></p><p>\cline{2-2} 29 & 29 \\</p><p></p><p></p><p>\cline{2-2} & 1</p><p></p><p>\end{array}$

$\begin{array}{r | l}</p><p></p><p>5 & 925 \\</p><p></p><p>\cline{2-2} 5 & 185 \\</p><p></p><p>\cline{2-2} 37 & 37 \\</p><p></p><p></p><p>\cline{2-2} & 1</p><p></p><p>\end{array}$

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

$\rule{200}3$

Therefore,

• 725 = 5 × 5 × 29

• 925 = 5 × 5 × 37

• 825 = 3 × 5 × 5 × 11

$\therefore$ HCF = 5 × 5 = 25

Therefore, the length of the largest which can measure the three dimensions of room exactly = 25 cm.

$\rule{200}3$