Triangles Test ...

The ratio of the areas of two similar triangles is equal to: 

The areas of two similar triangles are $$49 \ {cm}^{2}$$ and $$64 \ {cm}^{2}$$ respectively. The ratio of their corresponding sides is:

$$\Delta ABC \sim  \Delta PQR$$ and $$\displaystyle\frac{A( \Delta ABC)}{A( \Delta PQR)}=\dfrac{16}{9}$$. If $$PQ=18$$ cm and $$BC=12$$ cm, then $$AB$$ and $$QR$$ are respectively:

In figure, two lines segments $$AC$$ and $$BD$$ intersect each other at the point $$P$$ such that $$PA=6cm$$, $$PB=3cm$$, $$PC=2.5cm$$, $$PD=5cm$$, $$\angle APB={50}^{o}$$ and $$\angle CDP={30}^{o}$$. Then $$\angle PBA$$ is equal to:

In the adjoining figure, $$XY$$ is parallel to $$AC$$. If $$XY$$ divides the triangle into equal parts, then the value $$\cfrac{AX}{AB}=$$

In the figure, $$PQRS$$ is a parallelogram with $$PQ=15cm$$ and $$RQ=10cm$$. $$L$$ is a point on $$RP$$ such that $$RL:LP=2:3$$. $$QL$$ produced meets $$RS$$ at $$M$$ and $$PS$$ produced at $$N$$. Find the lengths of $$PN$$ and $$RM$$.

Find the length $$JN$$ in the given figure.

If $$\widetilde{BAD} \cong \widetilde{ADC}$$, then

$$P$$ and $$Q$$ are points on the sides $$AB$$ and $$AC$$ respectively of $$\triangle ABC$$ such that $$PQ\parallel BC$$ and divides the triangle into two parts of equal area. Find $$PB:AB$$.