In the given figure, triangles $\mathrm{ABC}$ and $\mathrm{PQR}$ are similar. Find the measures of the remaining sides of triangle $\mathrm{PQR}$.

Let $ABC$ be a triangle and $M$ be a point on side $AC$ closer to vertex $C$ than $A$. Let $N$ be a point on side $AB$ such that $MN$ is parallel to $BC$ and let $P$ be a point  on side $BC$ such that $MP$ is parallel to $AB$. If the area of the quadrilateral $BNMP$ is equal to $\frac{5}{18}$ of the area of $\mathrm{\Delta }ABC$, then the ratio $AM/MC$ equals

In a triangle $ABC$ with $\angle A<\angle B<\angle C,$ points $D,E,F$ are on the interior of segments $BC,CA,AB$ respectively. Which of the following triangles cannot be similar to the triangle $ABC$ ?

Consider the following figure shown below and choose which of the following equation is CORRECT about the similarity of both triangles?

In the given figure, if $DE\parallel BC, AD=2.5 cm, DB=3.5 cm$ and $EC=4.2 cm$, then the measure of $AC$ is:

In the given figure $AB=AC$ and $DB=DC$, Then $\angle ABD:\angle ACD$ will be