William W. answered • 03/06/20

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Let "s" be the length of the side of the square. Then the area of the square is s^{2}

Since "s" is the length of the side of the square, and it is also the side of the rectangle, then the area of the rectangle is (s)(6) or 6s.

Since the area of the rectangle is twice the area of the square then 6s = 2s^{2}

6s = 2s^{2}

2s^{2} - 6s = 0

2s(s - 3) = 0

s = 0 and s = 3

The s = 0 is meaningless in this case. So s = 3.

The square is then 3 inches x 3 inches and the rectangle is 6 inches x 3 inches

You could also draw a picture and logically determine the side of the square must be half of 6:

If the area of the rectangle is twice that of the square then you should be able to fit two squares in the rectangle:

So the side must be 6 because it takes two to equal the length 6.

David W.

03/06/20