Question:** A right triangle has legs of length 8 cm and 15 cm. If the length of each leg is increased by 2 cm, by how many square centimeters does the area increase?
["Title: How Area Increases When Legs of a Right Triangle Are Extended – Solving with Real Examples", "---", "### Understanding Area Changes When Legs of a Right Triangle Are Increased", "A classic geometry question often asked in math classes and standardized tests is: “How much does the area increase when the legs of a right triangle are extended?”\nUsing the specific case of a right triangle with legs measuring 8 cm and 15 cm, this problem becomes a perfect example to demonstrate how changes in triangle dimensions affect area. In this article, we’ll explore the math step-by-step, explain how to calculate area changes efficiently, and answer the key question: By how many square centimeters does the area increase when each leg is increased by 2 cm?", "---", "### Step 1: Original Area of the Right Triangle", "For a right triangle, the area is calculated using the formula:", "[\n\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "Here, the legs act as base and height. With legs of 8 cm and 15 cm:", "[\n\ ext{Original Area} = \frac{1}{2} \ imes 8 \ imes 15 = \frac{1}{2} \ imes 120 = 60 \ ext{ cm}^2\n]", "---", "### Step 2: New Leg Lengths After Increase", "Each leg increases by 2 cm, so:", "- New leg 1 = 8 cm + 2 cm = 10 cm\n- New leg 2 = 15 cm + 2 cm = 17 cm", "---", "### Step 3: New Area After Increase", "Using the same area formula:", "[\n\ ext{New Area} = \frac{1}{2} \ imes 10 \ imes 17 = \frac{1}{2} \ imes 170 = 85 \ ext{ cm}^2\n]", "---", "### Step 4: Calculating the Area Increase", "To find the increase in area, subtract the original area from the new area:", "[\n\ ext{Area Increase} = 85 \ ext{ cm}^2 - 60 \ ext{ cm}^2 = 25 \ ext{ cm}^2\n]", "---", "### Why This Calculation Matters", "This real-world example shows how a simple increase in side lengths alters triangle area dramatically. The multiplication of the two legs directly impacts the product used in the area formula. Increasing lengths not only grows the area but does so proportionally—making this triangle a perfect illustration of how geometric scaling affects area.", "---", "### Summary: Quick Recap", "| Measurement | Original Value | After Increase |\n|----------------------|----------------|----------------|\n| Leg 1 | 8 cm | 10 cm |\n| Leg 2 | 15 cm | 17 cm |\n| Original Area | 60 cm² | 85 cm² |\n| Area Increase | – | 25 cm² |", "---", "### Final Answer", "Increasing each leg of the right triangle by 2 cm increases the area by 25 square centimeters.", "---", "### Practice Tip", "This method applies to any right triangle: compute original and new areas using updated leg lengths, then find the difference. It’s a foundational skill useful for algebra, geometry, and competitive math preparation!", "---", "Keywords: right triangle area change, increase in triangle area, math problem-solving, geometry tutorial, how area changes with leg increase, practice geometry problems, area calculation formula, 8 cm and 15 cm triangle increase", "---", "Meta Description:\nDiscover how a right triangle’s area increases by 25 cm² when each leg, originally 8 cm and 15 cm, is boosted by 2 cm. Learn the step-by-step calculation and why triangle area responds dramatically to leg length changes.", "---", "Explore more geometry insights and solve similar problems by tuning into our full collection of math tutorials!"]
