Problem 65 - College Algebra Essentials

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=\frac{1}{2} h(a+b) \text { for } a$$

Step-by-Step Solution

Answer

The formula \(a = \frac{2A - bh}{h}\) represents the length of one base of a trapezoid given the area, the length of the other base, and the height.

Step 1: Identify the current formula and what it represents

The given formula \(A=\frac{1}{2} h(a+b)\) represents the area of a trapezoid. The goal is to rearrange this formula to isolate \(a\).

Step 2: Multiply both sides by 2

To remove the fraction from the equation, multiply both sides of the equation by 2. This results in \(2A = h(a + b)\).

Step 3: Distribute h

Distribute \(h\) to both \(a\) and \(b\) to get \(2A = ah + bh\).

Step 4: Isolate a

To isolate \(a\), subtract \(bh\) from both sides, which results in the equation \(a = \frac{2A - bh}{h}\).