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Height = \( \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \) mAfter sliding: base = 7 mNew height = \( \sqrt{13^2 - 7^2} = \sqrt{169 - 49} = \sqrt{120} = 2\sqrt{30} \) mBut \( 2\sqrt{30} \approx 10.95 \), so distance slid down:- 2\sqrt{30} \approx 12 - 10.95 = 1.05Exact:\Delta h = 12 - \sqrt{120} = 12 - 2\sqrt{30}But compute exactly:\sqrt{120} = \sqrt{4 \cdot 30} = 2\sqrt{30}So decrease in height is \( 12 - 2\sqrt{30} \) meters.