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If $c^{2} = a^{2} + b^{2}$ then write the value of $4 s (s - a) (s - b) (s - c)$ in terms of $a, b$ .

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$a^{3} b^{3}$

$\begin{array}{l} a^{2} b^{2} \end{array}$

$\frac{a}{b}$

answer is C.

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Detailed Solution

Given ${\dot{c}}^{2} = a^{2} + b^{2} \Rightarrow C = 90^{\circ}$

$\begin{array}{l} 4 s (s - a) (s - b) (s - c) = 4 Δ^{2} = 4 \cdot {(\frac{1}{2} a b \sin C)}^{2} \\ = 4 \cdot {(\frac{1}{2} a b \sin 90^{\circ})}^{2} = a^{2} b^{2} \end{array}$

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