The volume of the triangular prism is 54 cubic units. What is the value of x?
Solution:
Given, the volume of the triangular prism = 54 cubic units.
From the figure,
Base = 4 units
Height of the base triangle = x units
Height of the prism = 3x
The volume of the prism can be found using the formula,
Volume = base area × height of the prism
Base area = (1/2) × base × height of the base triangle
Base area = (1/2) × 4 × x
Base area = 2x
Now, 54 = 2x × 3x
6x2 = 54
x2 = 54/6
x2 = 9
Taking square root,
x = ±3
The negative value can be neglected, since length cannot be negative.
Therefore, the value of x is 3 units.
The volume of the triangular prism is 54 cubic units. What is the value of x?
Summary:
The volume of the triangular prism is 54 cubic units. The value of x is 3 units.