Study the example on the right to help you complete the problem below.
Solve the equation [tex]$A=\left(\frac{1}{2}\right) b h$[/tex] for [tex]$h$[/tex].
Answer (1)
Multiply both sides of the equation by 2: 2 A = bh .
Divide both sides of the equation by b : b 2 A = h .
Simplify to find the height h .
The solution is: h = b 2 A
Explanation
Understanding the Problem We are given the equation A = 2 1 bh and asked to solve for h . This means we want to isolate h on one side of the equation.
Multiply both sides by 2 To isolate h , we first multiply both sides of the equation by 2 to get rid of the fraction: 2 × A = 2 × ( 2 1 bh ) 2 A = bh
Divide both sides by b Next, we divide both sides of the equation by b to isolate h :
b 2 A = b bh b 2 A = h
Final Answer Therefore, we have solved for h :
h = b 2 A
Examples
Imagine you're designing a triangular sail for a boat. You know the area ( A ) you want the sail to be and the length of the base ( b ) of the sail. Using the formula h = b 2 A , you can calculate the height ( h ) the sail needs to be. This ensures your sail has the correct dimensions to catch the wind effectively. Understanding how to rearrange formulas like this is crucial in many design and engineering applications.
