To solve the equation [tex]\( A = b \cdot h \)[/tex] for [tex]\( b \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
A = b \cdot h
\][/tex]
2. To isolate [tex]\( b \)[/tex], you need to divide both sides of the equation by [tex]\( h \)[/tex]. This is because [tex]\( b \)[/tex] is being multiplied by [tex]\( h \)[/tex], and dividing by [tex]\( h \)[/tex] will cancel [tex]\( h \)[/tex] on the side containing [tex]\( b \)[/tex]:
[tex]\[
\frac{A}{h} = \frac{b \cdot h}{h}
\][/tex]
3. On the right-hand side of the equation, [tex]\( h \)[/tex] in the numerator and the denominator cancel each other out, leaving:
[tex]\[
\frac{A}{h} = b
\][/tex]
4. So, the solution to the equation [tex]\( A = b \cdot h \)[/tex] for [tex]\( b \)[/tex] is:
[tex]\[
b = \frac{A}{h}
\][/tex]
This matches one of your given choices. Therefore, the correct choice is:
[tex]\[
b = \frac{A}{h}
\][/tex]
