Question

एक 15.17 मीटर लंबे तथा 9.2मिटर चौड़े kmare के फर्श पर कम से कम कितना वर्गाकार टाइल्स लगेगी

Answer 1

Given:

The floor of a room is 15m 17cm long and 9 m 2cm broad

To find:

The least number of square tiles required to pave the floor of the room

Solution:

The length of the floor = 15 m 17 cm = (15×100) + 17 = 1500 + 17 = 1517 cm

The breadth of the floor = 9 m 2 cm =(9×100) + 2 = 900 + 2 = 902 cm

To find the length of the largest tile that can be used to pave the floor of the room, we have to calculate the HCF of 1517 & 902.

Factors:

1517 = 37 × 41

902 = 2 × 11 × 41

HCF:

HCF of 1517 & 902 = 41

Now,

The area of the floor of the room = length × breadth = 1517 × 902 = 1368334 cm²

and

The area of 1 square tile = side ² = 41² = 1681 cm²

Therefore,

The least no. of tiles required is,

= $\frac{Area \:of \:floor}{Area \:of \:1 \: tile}$

= $\frac{1368334}{1681}$

= $\bold{814}$

Thus, the least number of square tiles required to pave the floor of the room is → 814.

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