Unable to understnd the question

[archita]

Homework Statement

101. If A, B and C are the angles of a triangle and e1A, e1B and e1C are in Arithmetic Progression, then the
triangle is:
(A) Right angled but not isosceles (B) Isosceles but not right angled
(C) Equilateral (D) Right angled isosceles

Homework Equations

The Attempt at a Solution

Thought that e1A e1B e1C are angles tried as
e1A
e1B = e1A +d
e1C =e1A + 2d , wherd = common diff.
hence, sum of 3 int angles of triangle = 180
3(e1A + d) = 180
=> e1A + d = 60 degree
hence e1B=60
then i have no clue...
not able to get what e1B e1A e1C stands for...

 

[HallsofIvy]

First, you are NOT asked to find the angles! You are only asked which of "(A) Right angled but not isosceles (B) Isosceles but not right angled (C) Equilateral (D) Right angled isosceles" the triangle is.
It should be obvious that the angles are 60-d, 60, and 60+ d. Do you see that the triangle cannot be isosceles? It can be equilateral only if d= 0. Is "60, 60, 60" an arithmetic progression? If the triangle is a right triangle, then the largest angle, e1C, must be e1A+ 2d= 60+ d= 90 so d= 30. Now what is e1A?

 

[archita]

thnks halls. But answer is given it is an equilateral triangle . One more thing why are you taking angles as 60 -d ,60 60+d, I mean why 60?

 

[Dick]

thnks halls. But answer is given it is an equilateral triangle . One more thing why are you taking angles as 60 -d ,60 60+d, I mean why 60?

You got that E1A=60-d. Then E1B=60 and E1C=60+d. That's why 60. And I think there is more than one correct answer. 30-60-90 looks right angled but not isosceles to me.

 

[HallsofIvy]

thnks halls. But answer is given it is an equilateral triangle .

Yes, I said "It can be equilateral only if d= 0. Is "60, 60, 60" an arithmetic progression?"

One more thing why are you taking angles as 60 -d ,60 60+d, I mean why 60?

Because you had said, correctly, that
"e1A
e1B = e1A +d
e1C =e1A + 2d , wherd = common diff.
hence, sum of 3 int angles of triangle = 180
3(e1A + d) = 180
=> e1A + d = 60 degree
hence e1B=60"
If e1B= 60 and e1B= e1A+ d, then 60= e1A+ d and e1A= 60-d. From that e1C= e1A+ 2d= 60- d+ 2d= 60+ d.