Question

An area is paved with square tiles of certain size and the number of tiles required is 512. If the tiles had been 2 cm smaller each way, 800 tiles would have been needed to pave the same area. Find the size of larger tile.

Answer 1

Let the side of the larger square tile be x cm.

Area of one large tile = x²

Number of tiles = 512

So, total area:

512x²

If each tile is 2 cm smaller each way, side = (x − 2) cm.

Area of one smaller tile = (x − 2)²

Number of tiles = 800

Total area (same as before):

800 (x − 2)²

Since both pave the same area:

512x² = 800(x − 2)²

Divide both sides by 16:

32x² = 50(x − 2)²

32x² = 50(x² − 4x + 4)

32x² = 50x² − 200x + 200

18x² − 200x + 200 = 0

Divide by 2:

9x² − 100x + 100 = 0

9x² − 100x + 100 = 0

(9x − 10) (x − 10) = 0

`x = 10/9 or x = 10`

The size of the larger square tile is:

10 cm × 10 cm​