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Question

In the diagram the square has side length and the rectangle has dimensions (x+1) cm .x cm and (x +3) cm Given that the areas of the two shapes are equal, find the value of x.

Answer 1

square is x+1 by x+1

rectangle is x by x+3

area = (x+1)^2 = x(x+3)

x^2 + 2x + 1 = x^2 + 3x

x^2 - x^2 + 1 = 3x - 2x

x=1

square is 2 by 2 cm

rectangle is 1 by 4 cm

area of each = 4 cm^2