A rectangle is inscribed in a square, each of rectangle's vertex goes on each side of the square, sides of rectangle and diagonals of the square are parallel.
Find the sides of the rectangle, if one of its sides is 2 times the other, and the diagonal of the square is 12.
That's how I drew it, and since the diagonal is 12 and parallel to sides of the rectangle, I assumed the side of rectangle was the midline of the triangle made by the diagonal and therefore half of 12=6 and smaller part of rectangle half of that=3. Where did I make the mistake?
correct answer for the sides of rectangle is: 4 and 8
You made the mistake when you "assumed" rather than making sure that you used the information you were given.
You should start by observing that the two smaller triangles cut off the corners of the square have a hypotenuse which is half the length of the hypotenuse cut off by the larger pair of triangles. The configuration is then quite easy to analyse (you have a number of $45^{\circ}$ angles and can also draw a rather more accurate and more helpful diagram).