We are interested in the dimensions of a certain rectangle. This rectangle has length twice the side of the square and width three units less than the side of this square. If the two areas are equal, what are the rectangle's dimensions (w x h)
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let the sides of the square be S, the length of the rectangle will be 2S and the width will be S-3.
Area of square=S*S
Area of the rectangle= 2S(S-3)=2S^2-6S
but the areas are equal, therefore, 2S^2-6S=S^2
S(S-6)=0, meaning that S=0 or S-6=0, but S cannot be 0, therefore S-6=0; S=6
the dimensions of the rectangle are length=2(6)=12 and width S-3=6-3=3
area of rectangle is 3*12= 36 square units
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