To solve the equation \( A = \frac{1}{2}h(b + c) \) for \( b \), follow these steps:

1. Start by multiplying both sides by 2 to eliminate the fraction:
   \[
   2A = h(b + c)
   \]

2. Next, divide both sides by \( h \) to isolate the term with \( b \):
   \[
   \frac{2A}{h} = b + c
   \]

3. Finally, subtract \( c \) from both sides to solve for \( b \):
   \[
   b = \frac{2A}{h} - c
   \]

Thus, the solution for \( b \) is:

\[
b = \frac{2A}{h} - c
\]

Would you like further details or have any questions?

Here are some related questions that might interest you:

1. How would you solve for \( c \) in the equation \( A = \frac{1}{2}h(b + c) \)?
2. If \( A = 10 \), \( h = 4 \), and \( c = 3 \), what is the value of \( b \)?
3. How can this formula be used in geometry, specifically for finding the area of trapezoids?
4. What happens if \( h = 0 \) in the original equation? Is there a solution for \( b \)?
5. How would you solve for \( h \) in the equation \( A = \frac{1}{2}h(b + c) \)?

**Tip:** When solving equations, always perform the same operation on both sides to maintain equality.

Learn how to solve the equation A = 1/2h(b + c) for b in this step-by-step solution. This algebraic problem covers key concepts such as solving for a variable and manipulating equations, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation