Question : If in a $\triangle$ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{AD}{BD}$ = $\frac{3}{5}$. If AC = 4 cm, then AE is:

Question : In $\triangle$ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 16 cm and the length of AQ is 4 cm, then the length (in cm) of CQ is:

Question : $\triangle$ABC is similar to $\triangle$PQR. The length of AB is 16 cm and the length of the corresponding side PQ is 9 cm. If the area of $\triangle$ABC is 1024 sq. cm, what is the area of $\triangle$PQR?

Question : In the isosceles triangle ABC with BC is the unequal side of the triangle, and line AD is the median drawn from the vertex A to the side BC. If the length AC = 5 cm and the length of the median is 4 cm, then find the length of BC (in (cm).

Question : In $\triangle$ABC, D is the midpoint of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of ABC is equal to: