Question

the length,breadth and height of a room are 8m50cm, 5m75cm and 1m75cm respectively. Find the length of the longest tape which can measure the three dimensions of the room.​

Answer 1

Given :

• Length of a room = 8m 50cm.
• Breadth of a room = 5m 75cm.
• Height of a room = 1m 75cm.

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To find :

• The length of the longest tape which could measure the three dimensions of the room.

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How to proceed ?

For this question we will use the concept of HCF or GCD.

As,

$\bf\:Length~of~longest~tape~=~HCF~of~given~dimensions$

But for calculating HCF of 8m 50cm , 5m 75cm and 1m 75cm we need to convert them into same unit. So our first task would be to convert their units to cm. And then calculating their HCF, we will get our answer.

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Converting the units to cm :

We know,

⠀⠀⠀⠀⠀⠀1m = 100cm

So to convert m to cm we need to multiply the given length value by 100.

Therefore,

⠀⠀⠀⠀⠀⠀8m 50cm

$\sf\to\:(8 \times 100)cm + 50cm$

$\sf\to\:800cm + 50cm$

⠀⠀⠀⠀⠀⠀ $\bf\to\:850~cm$

Similarly,

⠀⠀⠀⠀⠀⠀5m 75cm

$\sf\to\:(5 \times 100)cm + 75cm$

$\sf\to\:500cm + 75cm$

⠀⠀⠀⠀⠀⠀ $\bf\to\:575~cm$

Again,

⠀⠀⠀⠀⠀⠀1m 75cm

$\sf\to\:(1 \times 100)cm + 75cm$

$\sf\to\:100cm + 75cm$

⠀⠀⠀⠀⠀⠀ $\bf\to\:175~cm$

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Calculating HCF :

For HCF I am following Prime factorization.

Prime factors of 850, 575 and 175 are as follows :

850 = 2 × 5 × 5 × 17

675 = 5 × 5 × 23

450 = 5 × 5 × 7

The common factors of 850, 575 and 175 are 5 and 5.

So,

⠀⠀HCF = 5 × 5 = 25 cm

$\small\red{\tt\pmb{⋆}}$ Hence longest tape is 25 cm which can measure the three dimensions of the room exactly.

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Note :

⠀⠀⠀ Scroll left to right to view the answer properly!~

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Answer 2

Answer:

Length of a room = 8m 50cm.

Breadth of a room = 5m 75cm.

Height of a room = 1m 75cm.

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