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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 A ladder leans against a wall, forming a right triangle with the ground. The ladder is 13 meters long, and the base is 5 meters from the wall. If the ladder slides so the base moves 2 meters farther out, how far does the top of the ladder slide down the wall?

📌 Initially:

📌 Base = 5 m, hypotenuse = 13 m

📌 Height = \( \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \) m

📌 After sliding: base = 7 m

📌 New height = \( \sqrt{13^2 - 7^2} = \sqrt{169 - 49} = \sqrt{120} = 2\sqrt{30} \) m

📌 But \( 2\sqrt{30} \approx 10.95 \), so distance slid down:

📌 - 2\sqrt{30} \approx 12 - 10.95 = 1.05

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