Question

It is desired to pave a rectangular courtyard of length 3.78 m and width 5.25 m by square titles of the same size. Find the largest size of the tile that can be fitted to cover the courtyard so that there is no need of breaking any tile. What is the number of tiles?
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Answer 1

Given:

Length of rectangular courtyard = 3.78 m = 378 cm

Breadth of rectangular courtyard = 5.25 m = 525 cm

Formula used:

Minimum number of tiles = (Area of rectangular courtyard)/(Area of square)

Area of rectangle = l × b

Area of square = a2

where,

l = length of rectangle

b = breadth of rectangle

Calculations:

Highest possible dimension of square = HCF of 378 and 525

⇒ 21 cm

Minimum number of tiles = (Area of rectangular courtyard)/(Area of square)

⇒ (l × b)/a2

⇒ (378 × 525)/(21)2

⇒ 450

∴ The minimum number of such tiles is 450.

Answer 2

Explanation:

Breadth of a rectangular courtyard =3.78m=378cm

Length of a rectangular courtyard =5.25m=525cm

Now, we have to find H.C.F os 378 and 525

378=2×3×3×3×7

525=5×5×3×7

Common factore=3×7

∴ H.C.F=21

Hence largest size of square tiles that can be paved exactly with square tiles is 21cm.