If `Delta` is the area of a triangle with side lengths ` a, b, c,` then show that as `Delta leq 1/4 sqrt((a + b + c) abc)` Also, show that the equality occurs in the above inequality if and only if `a = b = c`.

Explanation

To show that the area \( \Delta \) of a triangle with side lengths \( a, b, c \) satisfies the inequality

\[ \Delta \leq \frac{1}{4} \sqrt{(a + b + c) abc} \]

and that equality holds if and only if \( a = b = c \), we can follow these steps:

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