Question

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 the triangle is

• A. 2
• B. 3
• C. 1
• D. 4

Answer 1

Answer: (A)

2

Answer 2

Let A(0, 0), B(1, 0) & C(a, b) be the vertices of the triangle

Ž The product of the altitudes of the triangle is $\frac{|\beta|^{3}}{\alpha^{2} + \beta^{2}}$.

This is maximum for a = 0 & b = 1/2

Ž maximum value of 4 times the product of the altitudes = 2