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

Verified step by step guidance

1. Identify the formula given: \(A = \frac{1}{2}bh\). This is the formula for the area of a triangle, where \(A\) is the area, \(b\) is the base, and \(h\) is the height.
2. The problem asks to solve the formula for the variable \(b\), which means we want to isolate \(b\) on one side of the equation.
3. Start by eliminating the fraction. Multiply both sides of the equation by 2 to get rid of the denominator: \$2A = bh$.
4. Next, to isolate \(b\), divide both sides of the equation by \(h\): \(b = \frac{2A}{h}\).
5. Now the formula is solved for \(b\), expressing the base of the triangle in terms of the area and height.

Key Concepts

Solving Formulas for a Variable

This involves isolating the specified variable on one side of the equation. It requires using algebraic operations such as multiplication, division, addition, or subtraction to rewrite the formula in terms of the desired variable.

Area of a Triangle Formula

The formula A = (1/2)bh calculates the area of a triangle, where 'b' is the base length and 'h' is the height. Understanding this geometric context helps interpret the variables and the meaning of the formula.

Algebraic Manipulation Techniques

These techniques include multiplying both sides by a common denominator or dividing both sides by a coefficient to isolate variables. Mastery of these methods is essential for rearranging formulas accurately.