Questions: 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.

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.

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

Solution

Solution Steps

To solve the formula \( A = 2lw + 2lh + 2wh \) for \( h \), we need to isolate \( h \) on one side of the equation. This involves rearranging the terms and factoring out \( h \).

Solution Approach

Start by subtracting \( 2lw \) from both sides of the equation.
Combine the terms involving \( h \) on one side.
Factor out \( h \) from the terms on the right side.
Divide both sides by the remaining coefficient of \( h \) to isolate \( h \).

Step 1: Subtract \(2lw\) from both sides

Starting with the equation: \[ A = 2lw + 2lh + 2wh \]

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

Step 2: Factor out \(h\) on the right side

Combine the terms involving \(h\): \[ A - 2lw = 2h(l + w) \]

Step 3: Divide both sides by \(2(l + w)\)

Isolate \(h\) by dividing both sides by \(2(l + w)\): \[ h = \frac{A - 2lw}{2(l + w)} \]

Final Answer

\[ \boxed{h = \frac{A - 2lw}{2(l + w)}} \]

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