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

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

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

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

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

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

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

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

Would you like more details or have any other questions?

### Related Questions
1. How would you solve the formula for \( l \) instead of \( h \)?
2. What happens to \( h \) when \( l \) or \( w \) is increased while keeping the surface

Learn how to solve the formula A = 2lw + 2lh + 2wh for h. This problem involves geometry and algebra, focusing on deriving the height of a rectangular solid from its surface area formula. Suitable for students in Grades 9-12.

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