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?

Step-by-step solution

Among all triangles that have same perimeter, equilateral triangles are one that enclose maximum area. 24 3 =8 ~cm Here, A B=B C=C A= 24 3 =8 ~cm Area of A B C= 3 4 (B C)^2= 3 4 (8)^2=16 3 ~cm ^2A D is the altitude of the A B C . Then, Area of A B C= 1 2 B C A D 16 3 = 1 2 8 A D A D=4 3 ~cm