In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h

Verified step by step guidance

1. Identify the formula given: \(A = 2lw + 2lh + 2wh\), which represents the surface area of a rectangular prism, where \(l\) is length, \(w\) is width, and \(h\) is height.
2. Our goal is to solve the formula for the variable \(h\), meaning we want to isolate \(h\) on one side of the equation.
3. Start by grouping all terms involving \(h\) on one side: \(A = 2lw + 2lh + 2wh\). Subtract \$2lw\( from both sides to get \)A - 2lw = 2lh + 2wh$.
4. Factor \(h\) out of the right side: \(A - 2lw = h(2l + 2w)\).
5. Finally, divide both sides by \((2l + 2w)\) to isolate \(h\): \(h = \frac{A - 2lw}{2l + 2w}\).

Key Concepts

Solving Formulas for a Specific Variable

This involves rearranging an equation to isolate the desired variable on one side. It requires using algebraic operations such as addition, subtraction, multiplication, division, and factoring to rewrite the formula explicitly in terms of that variable.

Surface Area of a Rectangular Prism

The formula A = 2lw + 2lh + 2wh represents the surface area of a rectangular prism, where l, w, and h are the length, width, and height. It calculates the total area of all six faces by summing the areas of opposite sides.

Combining Like Terms and Factoring

When solving for h, it is important to group terms involving h and factor it out. This simplifies the equation and allows for isolating h by dividing both sides by the coefficient of h.