Question

One hundred tiles of a certain size are needed to pave a floor. If a tile, which measures 4 cm less on each side, will be used, 225 tiles will be needed. Find the size of the larger tile.

Answer 1

Let's assume the tiles are square, and each tile is x by x cm
so area of floor = 100x^2

then size of each smaller tile = x-4 by x-4

area with smaller tiles = 225(x-4)^2

225(x-4)^2 = 100x^2
take √
15(x-4) = 10x
15x - 60 = 10x
x = 12

So the larger tile is 12 cm by 12 cm
(smaller is 8 by 8)

Check:
using larger: area = 100(12by12) = 14400 cm^2
using smaller : area = 225(8by8) = 225(64) = 14400cm^2
Answer is correct!