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The base AB of a triangle is 1 and height h of C from AB is less than or equal to 1/2 . The maximum value of 4 times the product of the altitudes of triangle is .......

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Let A (0, 0), B (1, 0) and C (α ,β) be the vertices of the triangle. The product of the altitudes of the triangle is |β|3/α2 ,β2.

This is maximum for α = 0 and β = 1/2.

The maximum values of 4 times the product of the altitudes = 2. 

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