\frac{1}{2} \cdot 10 \cdot h = 45 \Rightarrow 5h = 45 \Rightarrow h = 9.

["How to Solve the Equation (\frac{1}{2} \cdot 10 \cdot h = 45) – Step-by-Step Explanation", "Understanding how to solve simple linear equations is a fundamental math skill that helps in numerous real-life applications—from calculating areas to solving for unknowns in physics and finance. In this article, we walk through solving the equation:", "[\n\frac{1}{2} \cdot 10 \cdot h = 45\n]", "and show step-by-step how it leads to the solution (h = 9).", "---", "### Step 1: Simplify the Left-Hand Side", "Start by simplifying the expression on the left side of the equation:", "[\n\frac{1}{2} \cdot 10 \cdot h = 45\n]", "Multiply (\frac{1}{2}) and 10:", "[\n\frac{1}{2} \cdot 10 = 5\n]", "So the equation becomes:", "[\n5h = 45\n]", "---", "### Step 2: Solve for (h)", "Now solve for (h) by isolating it on one side. Since (h) is multiplied by 5, divide both sides of the equation by 5:", "[\nh = \frac{45}{5} = 9\n]", "---", "### Final Answer", "[\nh = 9\n]", "---", "### Why This Equation Matters", "Equations like (\frac{1}{2} \cdot 10 \cdot h = 45) represent situations where a quantity ((h)) is part of a proportional relationship. Solving such equations helps confirm unknown values and supports decision-making in areas like budgeting, physics (force = mass × acceleration), and geometry (e.g., finding height from area).", "---", "### Summary", "- Simplify: (\frac{1}{2} \cdot 10 \cdot h = 5h = 45)\n- Solve: (h = \frac{45}{5} = 9)\n- Final answer: (\boxed{h = 9})", "Understanding these basic algebraic steps builds a strong foundation in problem-solving with equations.", "---", "Keywords: solve linear equation, understand algebra, step-by-step equation solving, fraction multiplication, multiplication property of equality, solve for variable, basic math problem-solving"]