Question

$\triangle A B C$ has different side lengths $a, b, c$. If $a^{2}, b^{2}, c^{2}$ as sides form another $\triangle P Q R$, then $\triangle A B C$ will always be

• A. acute angled triangle only
• B. obtuse angled triangle only
• C. sometimes acute or sometimes obtuse depending on values of $a, b $ and $c$
• D. none of these

Answer 1

Answer: (A)

Let $a > b > c$, given that $b+c > a$ and $b^{2}+c^{2} > a^{2}$
$\therefore b^{2}+c^{2}-a^{2} > 0$
$\therefore 2 b c \cos A > 0$
$\therefore \cos A > 0$
$\therefore A$ is acute angle.
Similarly $\cos B > 0, \cos C > 0$
So, $\triangle A B C$ is an acute angled triangle.