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!
