  
A
=
2
l
w
+
2
l
h
+
2
w
h
 , gives the surface area  
A
 , of a rectangular solid with length, width, and height,  
l
 ,  
w
 , and  
h
 , respectively. Solve the formula for  
w
 .

To solve the formula \( A = 2lw + 2lh + 2wh \) for \( w \), follow these steps:

### Step 1: Isolate the terms involving \( w \)
\[ A = 2lw + 2lh + 2wh \]

Subtract \( 2lh \) from both sides:
\[ A - 2lh = 2lw + 2wh \]

### Step 2: Factor out \( w \) from the right-hand side
\[ A - 2lh = 2w(l + h) \]

### Step 3: Solve for \( w \)
Divide both sides by \( 2(l + h) \):
\[ w = \frac{A - 2lh}{2(l + h)} \]

So, the formula for \( w \) is:
\[ w = \frac{A - 2lh}{2(l + h)} \]

This is the solution for \( w \) in terms of \( A \), \( l \), and \( h \).

Would you like more details or have any other questions?

### Related Questions
1. How would you solve the formula for \( l \) instead of \( w \)?
2. What is the physical interpretation of each term in the equation \( A = 2lw + 2lh + 2wh \)?
3. How would you apply this formula if one of the dimensions (e.g., \( h \)) is known to be zero?
4. Can you calculate \( w \) if the surface area \( A \), length \( l \), and height \( h \) are given?
5. How does changing one dimension, like \( l \), affect the width \( w \) if the surface area \( A \) is kept constant?

### Tip:
When solving for a variable, always try to isolate the variable step by step, using basic algebraic operations like addition, subtraction, multiplication, division, and factoring.

Learn how to solve the formula A = 2lw + 2lh + 2wh for width (w) in a rectangular solid with length (l), width (w), and height (h). This problem involves algebraic manipulation and surface area calculations. Suitable for students in Grades 9-12.

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