23. Dr. Evers is experimenting with light beams and prisms. He passes a beam of white light through a triangular prism which spreads the light out into its six rainbow colors. The bases of the prism are equilateral triangles. The surface area of this prism is 4,292 square millimeters. The area of each triangular face is 271 square millimeters. Which expression can be used to find h, the height, in millimeters, of the prism?
Answer: D
The expression that can be used to find h, the height, in millimeters, of the prism is (4,292-2(271))/3(25).
To determine the height of the prism, we need to account for the surface area and the area of the triangular faces. The correct expression properly adjusts the total surface area by subtracting the area of the two triangular faces, and then divides by the base area to isolate the height.
A) 4,292/3(25)
This option incorrectly uses the total surface area without subtracting the areas of the triangular faces. It assumes a division by the base area which does not reflect the actual structure of the prism.
B) 4,292/271
While this option divides the total surface area by the area of one triangular face, it does not account for the total surface area of the prism correctly. The height cannot be derived from this calculation as it does not consider the necessary adjustments for the other faces.
C) (4,292-271)/25
This expression subtracts only one triangular face's area from the total surface area, which is insufficient. The prism has two triangular faces, and thus this approach does not accurately represent the calculation needed to find the height.
D) (4,292-2(271))/3(25)
This option correctly subtracts the area of both triangular faces from the total surface area before dividing by the base area. By accounting for both triangular faces, it provides the appropriate formula to isolate and calculate the height of the prism.
Conclusion
The correct expression, (4,292-2(271))/3(25), effectively incorporates the total surface area and the areas of the triangular faces to solve for the height of the prism. All other options fail to correctly represent the necessary adjustments or calculations, making them unsuitable for determining the height. Thus, option D is definitively the right choice.