Measure the angle

Question

In a triangle, the measure of the greatest angle is square of the measure of the smallest angle, and the third angle is double of the smallest angle.

1) What is the equation of the triangle.

2) Solve the equation. 

3) Find value of the greatest angle.

4) Name the type of triangle with respect to angles.

Answer 1

Lex x = length of the smallest angle, then X² = length of the largest angle and 2x = length of teh middle angle.  The interior angles of a triangle always total 180 degrees so:

 

x² + 2x + x = 180

 

x² + 3x - 180 =0

 

(x+15)(x-12) = 0

 

x = -15 or 12, -15 is an impossible answer (an angle cannot be negative.

 

Smallest angle = 12, middle angle = 24, largest angle = 144.

 

It is an obtuse triangle