Question

mathematics progress check
the rectangular prism below has two congruent square faces and four congruent rectangular faces.
note: figure is not drawn to scale.
the line segment formed by connecting vertices e and b is 18 units long, the line segment formed by connecting vertices g and e is 13 units long, and the line segment formed by connecting vertices h and a is 18 units long.
if the rectangular prism is sliced by a plane that passes through vertices h, c, and a, which of the following best describes the resulting cross - section of the prism?
a. a rectangle with a length of 18 units and a width of 13 units
b. a triangle with side lengths of 18 units, 13 units, and 18 units
c. a square with side lengths of 18 units
d. a triangle with a height of 18 units and a base of 13 units

Explanation:

Step1: Understand cross - section concept

A cross - section is the shape obtained when a solid is sliced by a plane. When a plane passes through three non - collinear vertices (H, C, and A) of a rectangular prism, it forms a triangle.

Step2: Identify side lengths

The lengths of the line - segments connecting the vertices are given as: $HA = 18$ units, $GE=13$ units (and since the prism has congruent faces and edges, the relevant edge length for the cross - section related to the connection between the vertices of the cross - section is the same as the given edge lengths), and $EB = 18$ units. The side lengths of the triangle formed by the cross - section passing through H, C, and A are 18 units, 13 units, and 18 units.

Answer:

B. a triangle with side lengths of 18 units, 13 units, and 18 units