Problem 48

Question

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

Step-by-Step Solution

Verified
Answer
The value of 'b' in terms of 'A', 'h' and 'a' is \(b = \frac{2A - ha}{h}\). Yes, the formula describes the area of a trapezoid.
1Step 1: Isolate b in the equation
Start by isolating terms involving b. Multiply both sides by 2 to cancel out the fraction: \(2A = h(a+b)\).
2Step 2: Further isolate b
Next, you can distribute the h across the bracket, \(2A = ha + hb\). Then, subtract ha from both sides to complete the isolation for b: \(b = \frac{2A - ha}{h}\).
3Step 3: Final form of the equation
The final form of the equation after solving for b is: \(b = \frac{2A - ha}{h}\).