In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = (1/2)bh for b

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Understanding how to manipulate formulas is essential for solving for a variable, as it allows one to express the variable in terms of others.

Area of a Triangle

The formula A = (1/2)bh represents the area of a triangle, where 'A' is the area, 'b' is the base, and 'h' is the height. This formula is derived from the concept that the area of a triangle is half the product of its base and height. Recognizing this formula helps in understanding the geometric context of the problem and the significance of the variables involved.

Solving for a Variable

Solving for a variable means finding an expression that represents that variable in terms of others. In this case, we need to isolate 'b' in the equation A = (1/2)bh. This involves reversing the operations applied to 'b' and may require multiplying or dividing by other terms in the equation, which is a fundamental skill in algebra.