A square is a type of quadrilateral with four equal sides and four right angles. In the given question, it is mentioned that the quadrilateral has four equal sides and no right angles. A square cannot have no right angles, so it cannot be the correct answer. A rectangle is a type of quadrilateral with four right angles, but it is not mentioned in the question that the angles are right angles. Therefore, a rectangle cannot be the correct answer. A rhombus is a type of quadrilateral with four equal sides, but it does not necessarily have right angles. Since the question does not mention anything about the angles, a rhombus can be the correct answer. A trapezoid is a quadrilateral with at least one pair of parallel sides, which is not mentioned in the question. Therefore, a trapezoid cannot be the correct answer.