find ratio of perimeter of two triangles lies same base

Question

In a triangle ABC there is a point D on line AB. and points C and D are joined. It is given that Side AB is 50 and AD is 18. find the ratio of perimeter of triangles BCD and ACD?

I know I can find ratio of areas of these triangles but can I find ratio of perimeter of these triangles? should the triangles be similar to find ratio of perimeter?

Answer 1

Can't find the ratio of perimeter with the given information.

If triangles are similar then $$\frac{AD}{BD}=\frac{AC}{DC}=\frac{DC}{BC}.$$ In this case the ratio of perimeter is $$\frac{AD+CD+AC}{BD+CD+BC}=\frac{AD}{BD}$$

Answer 2

Hint: You can put the triangle into the circle, then use property of circle to find it. When triangles are similar , it’s very easy to see this ratio, but if you don’t have more information it’s not gonna be easy