Length = 45 units
Width = 50 units
Height = 1 unit
To find the length, width, and height of the rectangular prism, we can use the information given about the cross sections:
Cross section A
Cross section A is parallel to the base of the prism, so it is a rectangle with the same dimensions as the base. The area of the base is 90 units squared, so the length and width of the base must be factors of 90.
We know that the width of the prism is 50 units, so the length of the base must be 18 units.
Cross section B
Cross section B is perpendicular to the base and parallel to the sides of the prism, so it is a rectangle with the same height and width as the prism. The area of cross section B is 50 units squared, so the height and width of the prism must be factors of 50.
We know that the width of the prism is 50 units, so the height of the prism must be 1 unit.
Cross section C
Cross section C is perpendicular to the base and parallel to the front of the prism, so it is a rectangle with the same length and height as the prism. The area of cross section C is 45 units squared, so the length and height of the prism must be factors of 45.
We know that the height of the prism is 1 unit, so the length of the prism must be 45 units.
Therefore, the rectangular prism has a length of 45 units, a width of 50 units, and a height of 1 unit.
Question
The cross sections shown above are from a rectangular prism.
Cross section A is from a plane that is parallel to the base cutting through the prism. Cross section A has an area of 90 units squared.
Cross section B is from a plane that is perpendicular to the base and parallel to the sides of the prism cutting through the prism. Cross section B has an area of 50 units squared.
Cross section C is from a plane that is perpendicular to the base and parallel to the front of the prism cutting through the prism. Cross section C has an area of 45 units squared.
The prism in which the cross sections were taken has a length of
units, width of
units, and a height of
units.