SOLUTION: Please help me solve this problem: A rectangular counter is covered with 600 square tiles. The counter could have been covered with 400 tiles 1cm longer on a side. Fing the

Question 168387: Please help me solve this problem:
A rectangular counter is covered with 600 square tiles. The counter could have been covered with 400 tiles 1cm longer on a side. Fing the length of a side of the smaller tile.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rectangular counter is covered with 600 square tiles.
So the area of the counter is 600x^2 where x is the length of a side of a tile.
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The counter could have been covered with 400 tiles 1cm longer on a side.
So the area of the counter is 400(x+1)^2
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Find the length of a side of the smaller tile.
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Area 1st = Area 2nd
600x^2 = 400(x+1)^2
600x^2 = 400(x^2+2x+1)
600x^2 = 400x^2 + 800x + 400
200x^2 - 800x - 400 = 0
x^2 - 4x - 2 = 0
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x = [4 +- sqrt(16 - 4*-2)]/2
x = [4 +- sqrt(24)]/2
x = [4 +- 2sqrt(6)]/2
Positive solution:
x = 2 + 2sqrt(6) cm
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Cheers,
Stan H.

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