In ABC, mB > mC and mC > mA. Which side of ABC is longest?

The lengths of the sides of a triangle are 6, 8, and 12. If the length of the shortest side of a similar triangle is 10, what is the length of its longest side?

The lengths of corresponding sides of the two similar triangles are in a ratio 10/6 = 5/3.

For the larger triangle, the langest side length is therefore (5/3)x12 = 20

To determine which side of triangle ABC is the longest, we need to compare the measures of all three sides. Given the information that mB > mC and mC > mA, let's analyze the possibilities:

1. If mB > mC and mC > mA, it implies that side B is the longest side.

2. If mB > mC and mC = mA, it means that side B is the longest side.

3. If mB > mC and mC < mA, it indicates that side A is the longest side.

Therefore, based on the given information, we can conclude that either side B is the longest side or side A is the longest side, depending on the specific measures of the angles.