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प्रश्न
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.
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उत्तर
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.
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