Final answer:
A rectangle inscribed in a right triangle can be a scalene rectangle, square, or golden rectangle.
Step-by-step explanation:
A rectangle inscribed in a right triangle can take different forms. Let's go through the options:
A) Equilateral rectangle: This is not possible because an equilateral rectangle doesn't exist. An equilateral rectangle would have all sides of equal length, which is not possible in a right triangle.
B) Scalene rectangle: This is possible. A scalene rectangle is a rectangle with sides of different lengths. It can be inscribed in a right triangle in various ways, depending on the lengths of the sides of the right triangle.
C) Square: This is possible. A square is a special type of rectangle with all sides of equal length. If the right triangle is an isosceles triangle, with two equal legs, then a square can be inscribed in it.
D) Golden rectangle: This is possible. A golden rectangle is a rectangle with side lengths in the golden ratio, approximately 1.618. It can be inscribed in a right triangle, depending on the lengths of the sides of the right triangle.