Question

If $ c^2 = a^2 + b^2, a + b + c = 2s $ , then $ 4s(s-a)(s-b)(s-c) $ equals

• A. $ a^2b^2 $
• B. $ a^2c^2 $
• C. $ b^2c^2 $
• D. $ s^4 $

Answer 1

Answer: (A)

$c^{2}=a^{2}+b^{2}$
$\therefore \triangle A B C$ is an right angled triangle at $C$.
$\therefore 4 s (s-a)(s-b)(s-c)=4 \Delta^{2} $
$=4\left(\frac{1}{2} \times \text { base } \times \text { height }\right)^{2} $
$=a^{2} b^{2}$