In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. This relates to the Pythagorean theorem in right triangles, where the hypotenuse is the longest side opposite the right angle.
The relationship between triangle lengths and corresponding opposite angles is such that the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. This is because the size of an angle in a triangle is directly related to the length of its opposite side. The larger the angle, the longer the opposite side needs to be and vice versa for smaller angles and shorter sides.
Looking at the options provided, (d) The longest side is opposite the largest angle, and the shortest side is opposite the smallest angle is correct. This principle is especially clear in right triangles, where the hypotenuse is always the longest side and opposite the right angle, which is the largest angle in such triangles.
The Pythagorean theorem supports this by showing the relationship between the lengths of the sides, where a² + b² = c² with c being the hypotenuse, thus the longest side of a right triangle.