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Chapter 1: Problem 48

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 \(b\)

Short Answer

Expert verified
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.

Step by step solution

01

Isolate b in the equation

Start by isolating terms involving b. Multiply both sides by 2 to cancel out the fraction: \(2A = h(a+b)\).
02

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: \(b = \frac{2A - ha}{h}\).
03

Final form of the equation

The final form of the equation after solving for b is: \(b = \frac{2A - ha}{h}\).

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