Question

the volume of the triangular prism is 54 cubic units. what is the value of x? o 3 o 5 o 7 o 9

Explanation:

Step1: Recall volume formula for triangular prism

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base is a triangle with base length $4$ and height $x$, so $B=\frac{1}{2}\times4\times x = 2x$. The height of the prism is $3x$. Then $V=(2x)\times(3x)$.

Step2: Set up the equation

We know that $V = 54$. Substituting into the volume formula, we get $(2x)\times(3x)=54$. Simplifying the left - hand side gives $6x^{2}=54$.

Step3: Solve for $x$

Divide both sides of the equation $6x^{2}=54$ by $6$: $x^{2}=\frac{54}{6}=9$. Take the square root of both sides. Since $x$ represents a length, we consider the positive square root. So $x = 3$.

Answer:

A. 3