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DABC be a tetrahedron such that AD is perpendicular to the base ABC and angleABC=30^(@). The volume of tetrahedron is 18. If value of AB+BC+AD is minimum, then the length of AC is |
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Answer» `6sqrt(2-sqrt(3))` `rArr 18-1/12(AD.AB.BC)` `rArr AD.AB.BC=216` Now, `AB+BC + ADge3 (AD.AB.BC)^(1//3)` `rArr AB+BC+AD ge18` Minimum VALUE occurs when AB=BC=AD=6 Hence, `AC = sqrt(AB^(2)+BC^(2)-2AB.BC. cos30^(@))` `=6sqrt(2-sqrt(3))` |
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