Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm, and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:

Question : $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD: DB = 4:5$, $CD$ and $BE$ intersect each other at $F$. Find the ratio of the areas of $\triangle DEF$ and $\triangle CBF$.

Question : In $\triangle$ABC, D and E are points on AB and AC, respectively, such that DE || BC and DE divide the $\triangle$ABC into two parts of equal areas. The ratio of AD and BD is:

Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE : BC = 6 : 7. (Area of $\triangle {ADE}$ ) : (Area of trapezium BCED) = ?

Question : Let D and E be two points on the side BC of $\triangle ABC$ such that AD = AE and $\angle BAD = \angle EAC$. If AB=(3x+1) cm, BD = 9 cm, AC=34 cm and EC = (y + 1) cm, then the value of (x + y) is: