Question

The sides of a triangle are in the ratio 4 : 6 : 7. Then

• A. The triangle is obtuse-angled
• B. The triangle is acute-angled
• C. The triangle is right-angled
• D. The triangle is impossible

Answer 1

The correct option is B The triangle is acute-angled

Let ABC is a triangle with sides $a,b,c$.
if $c^2<a^2+b^2$ then $C$ is a acute angle.
$\therefore △ABC$ is a acute angled triangle.
Since, $a=4x,b=6x,c=7x$
$\Rightarrow c^2=(7x{)}^2=49x^2$ and
$a^2+b^2=(4x{)}^2+(6x{)}^2=16x^2+36x^2=52x^2$
$\therefore c^2<a^2+b^2$
$\Rightarrow \text{Given},△$ is a acute angled triangle.
Option B is correct.