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# 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 - Mathematics

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#### 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.

#### Solution

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 = 128 x2 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:
128 x2 = 200 (x – 2)2
128 x2 = 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.

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