Question

a cube is shown.
how can the cube be cut so that the cross section is a rectangle (but not a square)?
cut dropdown with options parallel, perpendicular to dropdown

Explanation:

Step1: Recall Cube Cross - Section Properties

A cube has all edges equal. If we cut a cube parallel to a face, the cross - section is a square (since the face of a cube is a square). If we cut the cube perpendicular to a face but not along the edges (for example, cutting from the mid - point of one edge to the mid - point of another non - adjacent edge on a different face), we can get a rectangle that is not a square. When we cut parallel to a face, the length and width of the cross - section are equal (as the face is a square), so the cross - section is a square. When we cut perpendicular to a face but in a way that the two dimensions of the cross - section are different (by not cutting along the edges or parallel to the faces), we get a rectangle (not a square). So we need to cut perpendicular to a face (or an edge) in a non - square - producing way. Wait, actually, if we cut the cube perpendicular to a pair of opposite faces but not along the lines that would make the cross - section a square. Wait, let's think again. The first dropdown has "parallel" and "perpendicular". If we cut parallel to a face, cross - section is square. So to get a rectangle (not square), we need to cut perpendicular (but not in the way that the cross - section is a square, but actually, when we cut perpendicular to a face but at an angle that the two sides of the rectangle are of different lengths. Wait, no. Let's consider the cube's edges. A cube has edges of length \(s\). If we cut parallel to a face, the cross - section has length and width equal to \(s\), so square. If we cut perpendicular to a face, but along a plane that intersects four edges, with two of the edges having length \(s\) and the other two having length different from \(s\)? No, actually, when we cut the cube perpendicular to a face (i.e., along a plane that is perpendicular to the face's plane) but not parallel to any face, for example, cutting from a point on one edge to a point on another edge that is not on the same face's edge, we can get a rectangle. So the first step is to realize that cutting parallel gives a square, so to get a non - square rectangle, we need to cut perpendicular.

Step2: Analyze the Dropdown Options

The first dropdown has "parallel" and "perpendicular". Since cutting parallel to a face gives a square cross - section, we need to choose "perpendicular" to get a rectangle (not a square). For the second dropdown, if we assume the second part is about the direction (like perpendicular to a face or an edge), but based on the first part, to get a rectangle (not square), we cut perpendicular (to a face, for example). So the first option in the first dropdown should be "perpendicular".

Answer:

First dropdown: perpendicular
(Assuming the second dropdown is related to the direction of the cut, but based on the first part, the key choice for the first dropdown is perpendicular to get a non - square rectangle cross - section.)