Common side with different ratio

Question

Two triangles share a common side. The lengths of the sides of the first triangle are in the ratio 5:6:7, while those of the second are in the ratio 4:9:11. If the lengths of all six sides are integers, what is the smallest possible length of this common side. Plz explain!

Answer 1

one common side

one triangle has 3 sides in ratio of 5/6/7

2nd with ration 4/9/11

what is the smallest the common side can be if all 6 sides are integers???

LCM of smallest sides is

4x5 = 20 is the smallest common side

1st triangle is 20, 24, and 28

2nd is 20, 45 and 55

20/24/28 = 5/6/7 and 20/45/55 = 4/9/11