Question

An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same area. Find the size of the larger tiles.

Answer 1

Let the size of the larger tiles be x cm.

Area of larger tiles = x² cm²

Number of larger tiles required to pave an area is 128.

So, the area needed to be paved = 128x² cm²  ...(1)

Size of smaller tiles = (x – 2) cm

Area of smaller tiles = (x – 2)² cm²

Number of larger tiles required to pave an area is 200.

So, the area needed to be paved = 200(x – 2)² cm²  ...(2)

Therefore, from (1) and (2), we have:

128x² = 200(x – 2)²

128x² = 200x² + 800 – 800x

72x² – 800x + 800 = 0

9x² – 100x + 100 = 0

9x² – 90x – 10x + 100 = 0

9x(x – 10) – 10(x – 10) = 0

(x – 10)(9x – 10) = 0

`x = 10,10/9`

If `x = 10/9`,

Then `x - 2 = 10/9 - 2`

= `(10 - 18)/9`

= `(-8)/9`

Which is not possible.

Hence, the size of the larger tiles is 10 cm.