Question : $\triangle PQR$ is an isosceles triangle and $PQ=PR=2a$ unit, $QR=a$ unit. Draw $PX \perp QR$, and find the length of $PX$.

Question : In a triangle ${ABC}, {AB}={AC}$ and the perimeter of $\triangle {ABC}$ is $8(2+\sqrt{2}) $ cm. If the length of ${BC}$ is $\sqrt{2}$ times the length of ${AB}$, then find the area of $\triangle {ABC}$.

Question : If for an isosceles triangle, the length of each equal side is $a$ units and that of the third side is $b$ units, then its area will be:

Question : An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendicular drawn from D on the sides AB and AC respectively of ABC. If $AP = a$ cm , $AQ = b$ cm and $\angle$BAD = 15°, $\sin$ 75°= ?

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is: