Question

A large hall measuring 2600 cmby 1680 cmhas to be paved with identical tiles.
(a) Find the side of the largest square tile that can be used to tile the entire floor without cutting any tile.
(b) Find the total number of such tiles needed to pave the entire floor.

Answer 1

Let we have square tiles of a certain length, which we will call

′

x

′

cm.

The area of each tile is x

2

cm

2

.

The total area paved would be 600x

2

cm

2

.

According to given question,

600x

2

=864(x−1)

2

⇒600x

2

=864x

2

−1728x+864

⇒264x

2

−1728x+864=0

⇒24(11x

2

−72x+36)=0

⇒11x

2

−66x−6x+36=0

⇒11x(x−6)−6(x−6)=0

⇒(x−6)(11x−6)=0

⇒x−6=0,11x−6=0

⇒x=6or

11

6

Hence, the length of tiles=x=6cm.

Hence, this is the answer.

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Answer 2

Answer:

Let we have square tiles of a certain length which we say x , cm .

The area of each tile is x = 2cm²

The total area paved should be 600x = 2cm²

According to the question

600×2

= 864(x-1)²

= 600×2

= 864×2

-1728+864=0

= 264×2

-1728+864=0

= 24(11x)²

-66x-6x+36=0

= 11x(x-6)-6(x-6)=0

= (x-6)(11x-6)=0

= x-6=0, 11x-6 = 0

= x=6

Hence, the length of tiles = x = 6cm