Sides of a triangle in arithmetic progression. Find possible values of common difference

Question

Question

If the sides of a triangle are in arithmetic progression with first term $1$ and common difference $d$ find the set of possible values of $d$

Attempt

I do not have much of a clue on how to go about solving this. I've tried letting the angles be $\theta,$ $\theta+\varepsilon$ and $\pi-2\theta-\varepsilon$ and using the sine rule, and even the cosine rule, but to no prevail.

Any hints would be very much appreciated!

Answer 1

Thank you dxiv and Zubin. I had forgotten all about them.

Using the triangle inequality (multiple times) we get $$-\frac{1}{3}< d< 1.$$

Answer 2

Hint: In any triangle, the sum of the lengths of any two of its sides must be strictly greater than the length of the third.