A 24cm long wire is bent to form a triangle with one of the altitude of the triangle having the greatest possible area?
Answers
Complete Question :- A 24 cm long wire is bent to form a triangle with one of the angles as 60°. What is the altitude of the triangle having the greatest possible area ?
Answer :-
Let us assume that, the sides of the ∆ are a ,b and c cm .
so,
→ Perimeter of ∆ = Length of wire
→ a + b + c = 24 .
now, for maximum area, using concept of AM ≥ GM we get,
→ a + b + c / 3 ≥ ³√abc
→ 24/3 ≥ ³√abc
→ 8 ≥ ³√abc
cube both sides,
→ 512 ≥ abc
for maximum possible area , a = b = c
→ 512 = a³
→ a = 8 cm .
since one angle is given 60° , and all sides are equal , rest two angles also equal to 60° .
therefore,
→ Altitude of the ∆ = (√3/2) * side = (√3/2) * 8 = 4√3 cm .
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