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The volume of a triangular prism is given by the formula [tex]V=\frac{1}{2} a b h[/tex], where [tex]a[/tex] is the altitude or height of the triangle, [tex]b[/tex] is the base of the triangle, and [tex]h[/tex] is the height of the prism.

Solve the formula [tex]V=\frac{1}{2} a b h[/tex] for [tex]b[/tex].

A. [tex]b=2 V a h[/tex]
B. [tex]b=\frac{2 V}{a h}[/tex]
C. [tex]b=2 V - a h[/tex]
D. [tex]b=\frac{a h}{2 V}[/tex]



Answer :

GinnyAnswer
Sure, let's solve the given formula for [tex]\( b \)[/tex].

The formula for the volume [tex]\( V \)[/tex] of a triangular prism is:
[tex]\[ V = \frac{1}{2} a b h \][/tex]

We need to solve this equation for [tex]\( b \)[/tex]. Follow these steps:

1. Start with the original formula:
[tex]\[ V = \frac{1}{2} a b h \][/tex]

2. Multiply both sides of the equation by 2 to eliminate the fraction:
[tex]\[ 2V = a b h \][/tex]

3. Divide both sides of the equation by [tex]\( a h \)[/tex] to isolate [tex]\( b \)[/tex]:
[tex]\[ b = \frac{2V}{a h} \][/tex]

So, the formula for [tex]\( b \)[/tex] in terms of [tex]\( V \)[/tex], [tex]\( a \)[/tex], and [tex]\( h \)[/tex] is:
[tex]\[ b = \frac{2V}{a h} \][/tex]

Therefore, the correct answer is option B:
[tex]\[ b=\frac{2V}{a h} \][/tex]

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