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

Step-by-step explanation:

Width of the room=3m 50cm=3.50m. To carpet the room,we need to find the area of the floor. =4×3.50=14 sq.

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 entire floor

Solution:

The dimensions of the floor of room denote a rectangle and its area is given by

Area = length × breadth

Area = $450*360$

∴ Area of room's floor = $1,62,000 cm^{2}$

On determining the HCF of 450 and 360, size of square marble can be found out.

450 = 2×3×3×5×5

360 = 2×2×2×3×3×5

HCF = 2×3×3×5 = 90

∴ Size of square marbles = 90 cm

Area of one square marble = Area of square = $size^{2}$

Area of one square marble = $90^{2}$ = $8100cm^{2}$

Minimum no. of square tiles needed to cover entire floor

= $\frac{Area of room's floor}{Area of one square marble}$

= $\frac{162000}{8100}$

= 20

Final Answer

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