In the figure given below `D E || B C` . If `A D=2. 4 c m` , `D B=3. 6 c m` and `A C=5c m` , Find `A E` .

In a A B C , D and E are points on the sides A B and A C respectively such that D E || B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=2\ c m , A B=6\ c m and A C=9\ c m , find A E . .

In a A B C , D and E are points on A B and A C respectively such that D E||B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .

In Figure if /_A D E=/_B show that A D E ~ A B C . If A D=3. 8 c m , A E=3. 6 c m , B E=2. 1 c m and B C=4. 2 c m , find D E .

In Figure, D E || B C in /_\ A B C such that B C=8c m , A B=6c m and D A=1. 5 c m . Find D E .

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If B D=2. 5 c m ,\ \ A B=5c m and A C=4. 2 c m , find D C . (ii) If B D=2c m ,\ \ A B=5c m and D C=3c m , find A C . (iii) If A B=3. 5 c m , A C=4. 2 c m and D C=2. 8 c m , find B D .

In a A B C , A D is the bisector of /_A , meeting side B C at D . If A D=5. 6 c m , B C=6c m and B D=3. 2 c m , find A C . (ii) If A B=10 c m , A C=6c m and B C=12 c m , find B D and D C .

In a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E// B C : A B=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m .

In Fig. 4.140, /_A B C=90o and B D_|_A C . If A B=5. 7 c m , B D=3. 8\ c m and C D=5. 4 c m , find B C . (FIGURE)

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x .