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Chapter 2: Problem 23

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

Short Answer

Expert verified
The solution for variable b is \(b = \frac{2A - ah}{h}\).

Step by step solution

01

Understand the Problem

The problem is to solve the formula \(A=\frac{1}{2} h(a+b)\) for b. This is the area of a trapezoid special formula. Area A, height h, and the lengths of the two parallel sides a and b are given. We need to isolate b in this equation.
02

Isolate the term with b

To isolate b, the first step is to eliminate the fraction by multiplying both sides of the equation by 2. This gives us \(2A = h(a + b)\).
03

Distribute h across the brackets

Distributing h across (a + b) will not change the equation but will bring us closer to isolating b. After the distribution, the equation becomes \(2A = ah + bh\).
04

Move ah to the other side

Subtract ah from both sides of the equation to isolate the term with b. This gives us \(2A - ah = bh\).
05

Solve for b

Finally, divide both sides of the equation by h to solve for b. So, the solution for b is \(b = \frac{2A - ah}{h}\).

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