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📰 Roots: \(x = 2\) and \(x = -\frac{1}{2}\). 📰 #### 2, \(-\frac{1}{2}\)Question: A weather radar detects a storm front forming a triangle with sides measuring 10 km, 13 km, and 15 km. What is the length of the shortest altitude? 📰 Solution: First, compute the area of the triangle using Heron's formula. The semi-perimeter $ s = \frac{10 + 13 + 15}{2} = 19 $ km. The area $ A = \sqrt{19(19-10)(19-13)(19-15)} = \sqrt{19 \cdot 9 \cdot 6 \cdot 4} = \sqrt{4104} = 64.07 $ km² (approximate). The shortest altitude corresponds to the longest side (15 km). Using $ A = \frac{1}{2} \cdot \text{base} \cdot \text{height} $, the altitude $ h = \frac{2A}{15} = \frac{2 \cdot 64.07}{15} \approx 8.54 $ km. For exact value, simplify $ \sqrt{4104} = \sqrt{4 \cdot 1026} = 2\sqrt{1026} $, but numerical approximation suffices here. Thus, the shortest altitude is $ \boxed{8.54} $ km. 📰 Surprise Your Palate Skills Fun Culinary School Games You Cant Ignore 1457581 📰 H265 Codec Reveal The Future Of Video Compression You Need To See 3699376 📰 Jonathan Lipnicki Movies 7829607 📰 Big Move In Mortgage Rates Today Nov 8 2025Experts Say Borrowers Better Watch Out 341498 📰 Desperately Seeking Answers The Office Of Civil Rights Complaints Reveals Shocking Details Inside 3833393 📰 Estimated Jackpot Powerball 825315 📰 Uc Davis Oasis 3651654 📰 Pero L Nunca Lleg El Giro Que Nunca Esperaste 4834526 📰 The Ultimate X Men Climax X Men The Last Stand Dont Miss This Legacy Climax 2730514 📰 2024 Update The Millionaire Estimate Behind Donald Trumps Wealth Surge 6714363 📰 Watch This Simple Bus Drawing Transform Into A Monstermind Blown 9713058 📰 A Glaciologist Is Using Remote Sensing To Monitor The Changes In Glacier Rectangular Sections In Greenland If Each Section Covers An Area Of 500 Square Kilometers What Is The Smallest Number Of Identical Rectangular Sections Needed To Cover A Glacier Of 20000 Square Kilometers Exactly 8104810 📰 Delta College Stockton 5036229 📰 Sydney Smiths Secret Exposure Naked And Unapologetic In Shocking Footage 6408951 📰 The Incredible War For The Planet Of The Apes This Twisted Sequel Outshocks The Original 3675981