Question

the bases of the prism below are right triangles. if the prisms height measures 6 units and its volume is 57.6 units³, solve for $x$.

Explanation:

Step1: Recall volume formula for prism

$V = Bh$, where $B$ is base - area and $h$ is height.

Step2: Calculate base - area

Since $V = 57.6$ and $h = 6$, then $B=\frac{V}{h}=\frac{57.6}{6}=9.6$.

Step3: Recall area formula for right - triangle base

The base is a right - triangle with area $B=\frac{1}{2}\times2.4\times x$.

Step4: Solve for $x$

Set $\frac{1}{2}\times2.4\times x = 9.6$. First, simplify the left - hand side: $1.2x = 9.6$. Then, divide both sides by $1.2$: $x=\frac{9.6}{1.2}=8$.

Answer:

$x = 8$