No.
"The lengths of adjacent sides can be different." True for a rectangle, not true for a square.
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No. There is no way you can cut one rectangle in half and only get one square. The other half would also have to be a square and this will only happen if the proportions are 1:2 and you cut the long sides.There are infinitely many ways to cut a rectangle in half none of which result in new rectangles. Only if the rectangle has proportions 1:2 can cutting it in half make a square, in fact the result could be two squares, not one.
No, rhombus refers to its shape, not the fact that is has four equal sides. You could call a rhombus an equilateral parallelogram by why would you want to? Also, would you then call a square a rhombic rectangle?
Assuming that the fact that it is a rectangle means that it cannot be a square, then it can have any value in the interval (0, 20.25) square units. This depends on whether the rectangle is a long thin shape or a near-square.
If the only known fact is the length of the diagonal then the width and length of the rectangle CANNOT be determined. The diagonal could be that of a square, or of a rectangle that is very long but quite narrow. Consequently at least one more fact is required such as; the dimension of either the length or the width, or the angle that the diagonal makes to the base of the rectangle or even the area of the rectangle.
It never changed! The word 'oblong' still exists as a non-square rectangle. Unfortunately the way shapes tends to be taught to pupils is through drawings rather than looking closely at properties; the latter identifies the fact that a rectangle is simply a quadrilateral with 4 right-angles. This means a square is a rectangle with equal sides and an oblong is a rectangle with unequal sides.