List the sides of each triangle from shortest to greatest So

List the sides of each triangle from shortest to greatest

Solution

Simple solution:

The length of sides can be arranged in the order of the measure of angles opposite the sides
or in other words: measure of sides is porportional to the measure to the angles opposite of them.

Since the angles are not visible clearly, use the following to understand the solution:

For a.
Hence, if angles R>Q>P then PQ>RP>RQ

Similarly, for ABC triangle , we have

If A>C>B then BC>AB>AC

If A=C > B then BC=AB>AC

If A=B=C, then AB=BC=CA