Question

If the sides of a triangle are in the ratio 4 : 6 : 7, then the

• A. triangle is obtuse angled
• B. triangle is acute angled
• C. triangle is right angled
• D. none of these

Answer 1

The correct option is B triangle is acute angled

Let the sides be $a=4x,b=6x$ and $c=7x$

Now we know if $a^2+b^2>c^2$ then triangle is acute angled

Here $c^2={\left(7x\right)}^2=49x^2$

$a^2+b^2={\left(4x\right)}^2+{\left(6x\right)}^2=50x^2\Rightarrow a^2+b^2>c^2$

So the triangle is acute angled.

Hence option $B$ is correct.