Answer:
18 cm
Step-by-step:
The formula for the volume of a triangular prism is given by:
V_triangular_prism = (1/2) * base * height * length
where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.
We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:
432 = (1/2) * 36 * height * length
height * length = 24
Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:
V_rectangular_prism = length * width * height
We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:
432 = length * width * height
432 = length * width * (24/length)
432 = 24 * width
width = 18
Therefore, the base side length of the rectangular prism needs to be 18 cm.
Hope this helps!