Question

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

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

Answer 1

Answer: (A)

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