Question

The diagram shows a cube of side length 4 inches. A is a vertex of the cube, while B and C are located on opposite edges of the cube with both B and C being 1 inch from the nearest vertex.

If a plane including the points A, B, and C cuts through the cube, what is the shape of the resulting cross section?

an isosceles triangle
a rectangle
a square
a rhombus
a hexagon

Answer 1

we will get an isosceles triangle as a result.

Explanation:

when the point A is joined to B and C we will get the side AB and AC of equal length.

length of AB and AC could be calculated easily with the help of pythagorean theorem where the base and perpendicular are of length 4in and 1in .

when we will cut a plane including the the points A,B and C we will get a triangle whose sides AB and AC are equal but BC would be of distinct length.

Hence, the resultant figure will be an isosceles triangle.