Question

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

Answer 1

We don't need the length AND width of the square.  One number
will be enough for an answer, because all sides of a square have
the same length.  Let's call that number ' M ' (for 'mystery number').

-- The area of the square is  M² .

The question says that ...
-- The length of the rectangle is  2M .
-- The width of the rectangle is  (M - 3) .

Therefore ...
-- The area of the rectangle is  (2M)(M - 3)  =  2M² - 6M .

The question also says that ...
-- The areas of the square and the rectangle are equal:

So                                            2M² - 6M = M²

Subtract  M²  from each side:    M² - 6M = 0

Divide each side by  M :            M  -  6  =  0

Add  6  to each side :                 M  =  6 .


Check:

Assume ... Side of the square = 6

Then ...
Area of the square = 6² = 36 .
Length of the rectangle = (6 x 2) = 12
Width of the rectangle = (6 - 3) = 3
Area of the rectangle = (12 x 3) = 36

                 36  =  36                  yay!