Question

Angles of a triangle are in the ratio 4 : 6 : 5. The triangle is :

• A. an acute angles triangle
• B. an obtuse angled triangle
• C. right angled triangle
• D. isosceles triangle

Answer 1

The correct option is A an acute angles triangle

Let the angles be $4x,6x$ and $5x$

$4x+6x+5x={180}^{\circ }$

$15x={180}^{\circ }$

$\Rightarrow x={12}^{\circ }$

So the angles are

$4\times {12}^{\circ }={48}^{\circ }5\times {12}^{\circ }={60}^{\circ }6\times {12}^{\circ }={72}^{\circ }$

All the angles are less then $90$

So triangle is an acute angled triangle.