Question

In $△ABC$. If $c^2=a^2+b^2$, $2s=a+b=c$, then $4s(s-a)(s-b)(s-c)$

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

Answer 1

The correct option is D $a^2{b}^2$

$2s=a+b+c$

$s=\frac{a+b+c}{2}$

By Heron's formula

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

$a^2+b^2=c^2$

Area = $\frac{1}{2}\times a\times b$

$\therefore \sqrt{s(s-a)(s-b)(s-c)}=\frac{1}{2}\times a\times b$

of squaring both sides

$\Rightarrow s(s-a)(s-b)(s-c)=\frac{1}{4}{a}^2{b}^2$

$\Rightarrow 4s(s-a)(s-b)(s-c)=a^2{b}^2$.