Question

What is the minimum number of square marbles required to title a floor of length 5 m 78 cm and width 3 m 74 cm?

Answer 1

Hi there!
Here's the answer:

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SOLUTION:

As mentioned in the question,
The marbles used are of square shape

=> Length of marble = width of the marble


Since, Total Marbles are to be used, the side of the square should be a factor of 5m 78cm and 3m 74cm

5m 78cm = 500cm + 78cm = 578cm
3m 74cm = 300cm + 74cm = 374cm


Now,
Find HCF of 374 and 578

Using Division Method of finding HCF

374) 578 ( 1
……… 374
---------------------------
………204) 374 ( 1
……………… 204
-------------------------------
……………… 170) 204 ( 1
……………………… 170
------------------------------------------
…………………………[[ 34]] ) 170 ( 5
…………………………………… 170
--------------------------------------------------
…………………………….……… [ 0 ]

•°• HCF(374 , 578) = 34

•°• Side of square Marble is 34 cm

No. of Such square Marbles required
= $\frac{374×578}{34×34}$
= 17 × 11
= 187


•°• $\underline{187\: Marbles}$ are required to title a floor of length 5 m 78 cm and width 3 m 74 cm.


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Hope it helps