The question asks to solve for $b$ given the equation:

$A = \frac{1}{2} b h$

Steps to solve for $b$:

1. Start with the equation: $A = \frac{1}{2} b h$
2. Multiply both sides by 2 to eliminate the fraction: $2A = b h$
3. Finally, divide both sides by $h$ to solve for $b$: $b = \frac{2A}{h}$

So, the correct expression for $b$ is $\frac{2A}{h}$.

Looking at the provided options in the image, the correct answer corresponds to the third option: $b = \frac{2A}{h}$

Would you like further details on this solution or have any other questions?

Here are 5 related questions to explore this concept further:

1. How would you solve for $h$ instead of $b$ in the same formula?
2. What kind of shape or geometric figure does this formula likely represent?
3. How would you apply this formula to find $b$ if the area $A$ and height $h$ are given specific values?
4. Can this formula be rearranged to express $A$ in terms of $b$ and $h$?
5. How would you modify this formula if the area formula changes, for example, for a circle or a different geometric figure?

Tip: Always isolate the variable you want to solve for by performing inverse operations step by step.