Is it possible for a cross section of a cube to these shapes....

-pentagon
-isosceles triangle
-scalene triangle
..... If so, please describe how the plane intersects the cube.

Thanks!!!!

If you had a iscocles triangle and the vertex was 21y+13 and the bottom angle which is <b and was 6y+1 what would <a be and what would y be?

Yes, it is possible for a cross section of a cube to have these shapes - a pentagon, an isosceles triangle, and a scalene triangle. To understand how the plane intersects the cube, let's go through each shape individually:

1. Pentagon:
For a cross section of a cube to be a pentagon, the cutting plane must intersect at least 5 edges of the cube. The pentagon's vertices would be the points where the plane intersects the cube's edges.

2. Isosceles Triangle:
To have an isosceles triangle as a cross section, the cutting plane must intersect exactly 3 edges of the cube. The resulting triangle would have two equal sides and one different side.

3. Scalene Triangle:
To obtain a scalene triangle, the cutting plane must intersect 3 edges of the cube, but this time, all three sides of the triangle would be different lengths.

The orientation and position of the cutting plane within the cube determine the specific shape of the cross section. It's important to note that there can be endless possibilities for the orientation and position of the cutting plane that could result in these shapes.