In $\Delta XYZ$,the midpoints of the sides are $A, B$ and $C$. In $\Delta ABC$,the midpoints of the sides are $P, Q$ and $R$. If the area of $\Delta ABC$ is $24$,find the area of $\Delta XYZ$ and $\Delta PQR$.

If $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow XZY$,then $BC^2 : YZ^2 = \ldots \ldots \ldots$ (Wait,the question asks for $ABC : XYZ = BC^2 : \ldots$ which refers to the ratio of areas). Given $\Delta ABC \sim \Delta XZY$,the ratio of their areas is equal to the ratio of the squares of their corresponding sides. Thus,$\frac{\text{Area}(\Delta ABC)}{\text{Area}(\Delta XZY)} = \frac{BC^2}{ZY^2}$.

............... is not a condition for the similarity of two triangles.

If $S$ is a point on side $PQ$ of a $\triangle PQR$ such that $PS = QS = RS$,then

In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $AB : BC = 3 : 4$,find $AB : AC$.

In rectangle $ABCD$,$AB = 2.4$ and $BC = 3.2$. Then,$AC = \ldots$