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 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.
$Areaoflargertiles=x^{2}c{m}^2$
Number of larger tiles required to pave an area is 128.
So, the area needed to be paved $=128x^2\times c{m}^2\dots .$ (1)
Size of smaller tiles = (x – 2)cm
Area of smaller tiles =$(x–2{)}^{2}c{m}^2$
Number of larger tiles required to pave an area is 200.
So, the area needed to be paved $=200(x–2{)}^2\times c{m}^2\dots$. (2)
Therefore, from (1) and (2), we have:
$128x^2=200(x–2{)}^2$
$128x^2=200x^2+800–800x$
$72x^2–800x+800=0$
$9x^2–100x+100=0$
$9x^2–90x–10x+100=0$
9x(x – 10) – 10(x – 10) = 0
(x – 10)(9x – 10) = 0

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