Question

in the right triangular prism below, $overline{bg}perpoverline{fc}$. the volume of the prism is 900 cubic centimeters. the height of the prism is 15 centimeters and the height of the triangular base is 10 centimeters. what is the length of edge $fc$? cm

Explanation:

Step1: Recall volume formula for prism

$V = Bh$, where $V$ is volume, $B$ is base - area, and $h$ is height of prism.
Given $V = 900$ cm³ and $h = 15$ cm. First, find the area of the triangular base $B$.
$B=\frac{V}{h}=\frac{900}{15}=60$ cm².

Step2: Recall area formula for triangle

The area of a triangle $B=\frac{1}{2}\times base\times height$.
The height of the triangular base is $BG = 10$ cm. Let the base of the triangular base (edge $FC$) be $x$.
We know $B = 60$ cm² and $B=\frac{1}{2}\times x\times10$.
Set up the equation $\frac{1}{2}\times x\times10 = 60$.

Step3: Solve the equation for $x$

First, simplify the left - hand side of the equation: $5x=60$.
Then, divide both sides by 5: $x = 12$ cm.

Answer:

12