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Home » Let the integers be x and x+1. Then, (x+1)² - x² = 35. - Londonproperty

Let the integers be x and x+1. Then, (x+1)² - x² = 35. - Londonproperty

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}

📌 A = \sqrt{7056} = 84 \text{ cm}^2

📌 The shortest altitude corresponds to the longest side, which is 15 cm. Using the formula for area:

📌 A = \frac{1}{2} \cdot \text{base} \cdot \text{height} \Rightarrow 84 = \frac{1}{2} \cdot 15 \cdot h

📌 h = \frac{84 \cdot 2}{15} = \frac{168}{15} = 11.2 \text{ cm}

📌 \boxed{11.2}

📌 Question: A primatologist studying primate spatial reasoning observes a triangular enclosure with sides of 9 cm, 12 cm, and 15 cm. If the enclosure is transformed into an equilateral triangle with the same perimeter, by how many square centimeters does the area increase?

📌 Solution: The perimeter of the original triangle is:

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