In a ` A B C` , point `D` is on side `A B` and point `E` is on side `A C` , such that `B C E D` is a trapezium. If `D E : B C=3:5` , then Area`( A D E): A r e a( B C E D)=` `3:4` (b) `9: 16` (c) `3:5` (d) `9: 25`

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=2/5 , then A r e a( A B C): A r e a( D E F)= 2:5 (b) 4: 25 (c) 4: 15 (d) 8: 125

In A B C , D and E are points on side A B and A C respectively such that D E B C\ and A D : D B=3:1 . If E A=3. 3 c m , then A C= 1. 1 c m (b) 4c m (c) 4. 4 c m (d) 5. 5 c m

D and E are points on sides AB and AC respectively of DeltaA B C such thata r" "(D B C)" "=" "a r" "(E B C) . Prove that D E" "||" "B C .

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 D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

A B C is a triangle. D is a point on A B such that A D=1/4A B and E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B Cdot

A B J H , J D E F , A C E G are squares. (B C)/(A B)=3 . (A r e a B C D J)/(A r e a H J F G)=? (FIGURE) 1/9 (b) 1/3 (c) 1 (d) 3

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 (ii) If A D=8 c m , A B=12 c m and A E=12 c m , find C E . (iii) If A D=4 c m , D B=4. 5 c m and A E=8 c m , find A C .