Answer:
9 feet
Step-by-step explanation:
Given:
A prism with a triangular base has a volume of 432 cubic feet.
The height of the prism is 8.
The triangle base has a base of 12 feet.
Question asked:
The height of the triangular base of the prism = ?
solution:
Volume of triangular prism = [tex]Area of triangle \times height[/tex]
[tex]432 = Area of triangle \times8[/tex]
Dividing both side by 8
[tex]54 = Area of triangle[/tex]
[tex]54 =[/tex] [tex]\frac{1}{2} \times base \times height[/tex]
[tex]54 = \frac{1}{2} \times12\times height\\54 = \frac{12}{2} \times height[/tex]
Multiplying both side by 2
[tex]108 = 12 \times height[/tex]
Dividing both side by 12
[tex]9 = height[/tex]
Thus, height of the triangular base of the prism is 9
