The angles of a triangle in the ratio 4:3:14, the triangle is a) Isosceles triangleb) Obtuse trianglec) Equilateral triangled)A right angled triangle

Given: The angles of a triangle in the ratio 4:3:14

To find: The type of triangle

Solution:
 The angles are in the ratio 4:3:14

Let the angles be $4x, 3x, 14x$

We know sum of angles of a triangle is $180^{\circ}$

So, $4x+3x+14x = 180^{\circ}$

$21x = 180^{\circ}$

$x= \frac{180^{\circ}}{21}$

$x= \frac{60^{\circ}}{7}$

So, the angles are $4\times\frac{60^{\circ}}{7}, 3\times\frac{60^{\circ}}{7},14\times\frac{60^{\circ}}{7}$

They are  $\frac{240^{\circ}}{7},\frac{180^{\circ}}{7},120^{\circ}$

One angle is $120^{\circ}$ which is an obtuse angle(Greater than 90)

So, the given triangle is obtuse triangle.

Answer is b

Tutorialspoint

e

Updated on: 10-Oct-2022

66 Views

Kickstart Your Career

Get certified by completing the course

Get Started