To determine the best description of the cross section formed by a vertical plane that intersects the right face and the vertex of the pyramid, let's analyze the information provided.
A vertical plane that intersects the right face of the pyramid and the vertex will create a two-dimensional figure. The definition of the cross section depends on:
- The shape of the base of the pyramid (which is not specifically mentioned, but let's assume it's rectangular based on the provided dimensions).
- The intersection of the vertical plane.
Given that we are cutting through one of the triangular faces of the pyramid from the vertex to the base, this would typically produce a triangular cross section.
Now, let's evaluate the options:
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A. An isosceles triangle with base length equal to the width of the base and height equal to the height of the pyramid.
- This is incorrect because the height of the triangular cross-section will not be equal to the height of the pyramid.
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B. A rectangle with length and width equal to the length and width of the base of the pyramid.
- This is incorrect because the cross-section is formed by cutting through the pyramid, not looking at the full base.
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C. An isosceles triangle with base length equal to the width of the base and height less than the height of the pyramid.
- This is the correct choice. The base of the triangle will equal the width of the pyramid's base, and the height of the triangle will be less than the full height of the pyramid.
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D. An equilateral triangle with base length equal to the width of the base and height less than the height of the pyramid.
- This is incorrect unless specified that the triangle is equilateral, which is not generally the case for a pyramid.
Given this analysis, the best statement that describes the cross section is:
C. An isosceles triangle with base length equal to the width of the base and height less than the height of the pyramid.