Question

The floor of a room is 4m 50cm long and 3m 60cm broad. Find the minimum number of square marbles of the same size needed to cover the entire floor​

Answer 1

Answer:

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Answer 2

Given:

Length of room $= 4m 50cm$

                           $= 4.5m\\ = 450cm$

Breadth of room $= 3m 60cm$

                            $= 3.6m \\= 360cm$

To find:  Minimum no. of square marbles to cover the entire floor.

Solution:

Know that, the dimensions of the floor of the room denote a rectangle and its area is given by,

Area = length × breadth

Area $\[ = 450 \times 360\]$

∴ Area of room's floor $\[ = 162000c{m^2}\]$

Find the HCF of 450 and 360, to find the size of square marble.

$\[\begin{array}{l}450 = 2 \times 3 \times 3 \times 5 \times 5\\360 = 2 \times 2 \times 2 \times 3 \times 3\\HCF\left( {450,360} \right) = 2 \times 3 \times 3 \times 5\\ \Rightarrow HCF\left( {450,360} \right) = 90\end{array}\]$

Understand that, the size of square marbles $= 90$ cm.

Calculate the area of one square marble.

Area of one square marble$\[ = {\left( {Side} \right)^2}\]$

                                             $\[\begin{array}{l} = {90^2}\\ = 8100c{m^2}\end{array}\]$

Find the minimum no. of square tiles needed to cover the entire floor.

$\[\begin{array}{l} = \frac{{Area\,\,of\,room's\,floor}}{{Area\,\,of\,one\,\,square\,\,marble}}\\ = \frac{{162000}}{{8100}}\\ = 20\end{array}\]$

Hence, the minimum number of square marbles of same size needed to cover the entire floor of a room with dimensions 450cm × 360cm is $20.$