= \frac{1}{2} \times 15 \times h \Rightarrow h = \frac{84 \times 2}{15} = \frac{168}{15} = 11.2

["Understanding the Formula: Solving for ( h ) in (\frac{1}{2} \ imes 15 \ imes h) to Find the Height", "When solving equations involving geometry, one common pattern emerges: multiplying dimensions to find an unknown. A classic example is the area formula for a triangle:", "[\n\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "In this equation, if we know the area and the base, solving for the height becomes a simple algebraic step — and this is exactly the kind of problem often presented in middle school math or basic algebra practice.", "### The Problem Explained", "Let’s break down the equation:\n[\n\frac{1}{2} \ imes 15 \ imes h\n]", "Here, 15 represents the base length, and ( h ) is the unknown height we want to solve for. Suppose we know the area of a triangular shape, and we’re given this expression—perhaps from a word problem or a geometry exercise.", "For instance:\nIf the area is ( A ), then:", "[\nA = \frac{1}{2} \ imes 15 \ imes h\n]", "To isolate ( h ), rearrange the formula:", "[\nh = \frac{2A}{15}\n]", "But in our case, the problem simplifies to a direct calculation when certain values are provided:", "We’re told:", "[\n\frac{1}{2} \ imes 15 \ imes h = 84 \ imes 2\n]", "First, compute the right-hand side:", "[\n84 \ imes 2 = 168\n]", "So the equation becomes:", "[\n\frac{1}{2} \ imes 15 \ imes h = 168\n]", "Multiply both sides by 2 to eliminate the fraction:", "[\n15 \ imes h = 336\n]", "Then divide by 15:", "[\nh = \frac{336}{15} = 11.2\n]", "Or, writing it as a simplified fraction:", "[\nh = \frac{168}{15} = 11.2\n]", "### Why This Formula Matters", "This kind of algebraic rearrangement is foundational in solving real-world geometry problems — like calculating the height of a roof peak, the slope of a triangular roof section, or the steepness of a triangular plot. By isolating variables and simplifying expressions, students develop numerical reasoning and algebraic fluency.", "### Summary", "- The expression (\frac{1}{2} \ imes 15 \ imes h) models the area of a triangle.\n- Known area values allow solving for unknown height using division.\n- Step-by-step algebra confirms that ( h = 11.2 ), showing how fractions and multiplication interact in geometry.", "Understanding these steps helps build confidence in math and prepares learners for more advanced algebra and real-life problem solving.", "---", "Keywords: solve for h, triangle area formula, algebra basics, linear equations, geometry problem solving, fractions and multiplication, converting expressions to decimal"]