Sure, let's solve the formula for the base [tex]\( b \)[/tex] given the formula for the area of a triangle [tex]\( A = \frac{1}{2} b h \)[/tex].
Here's the step-by-step solution:
1. Start with the given formula:
[tex]\[
A = \frac{1}{2} b h
\][/tex]
2. Eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[
2A = b h
\][/tex]
This step helps to get rid of the [tex]\(\frac{1}{2}\)[/tex] factor.
3. Solve for [tex]\( b \)[/tex] by isolating it:
To isolate [tex]\( b \)[/tex], divide both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[
b = \frac{2A}{h}
\][/tex]
So, the formula for solving for the base [tex]\( b \)[/tex] in terms of the area [tex]\( A \)[/tex] and the height [tex]\( h \)[/tex] is:
[tex]\[
b = \frac{2A}{h}
\][/tex]
This is the expression that gives the value of the base [tex]\( b \)[/tex] when you know the area of the triangle and its height.
