We are interested in the dimensions of a certain square. A rectangle has length triple the side of this square and width two units less than the side of this square. If the two areas are equal, what are the square's dimensions (w x h)

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let the side of the square be s, then the rectangle has length 3s and width s-2.

the area of square is s*s=s^2 and that of the rectangle is 3s(s-2)=(3s^2-6s).

the areas are equal, therefore 3s^2-6s=s^2

3s^2-s^2-6s=0

2s^2-6s=0

2s(s-3)=0, s=0 or s=3.

then the squares dimension is 3 by 3. Hence the area of square is 9 square units

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