Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 8 cm

Option 4: 11 cm

Question : $\triangle BAC\sim \triangle PQR$. The area of $\triangle BAC$ and $\triangle PQR$ is 25 cm² and 36 cm² respectively. If BA = 4 cm, then what is the length of PQ?

Option 1: 5.8 cm

Option 2: 4.2 cm

Option 3: 4.8 cm

Option 4: 5 cm

Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 20 cm

Option 4: 22 cm

Question : In a $\triangle ABC$, if $\angle A=90^{\circ}, AC=5 \mathrm{~cm}, BC=9 \mathrm{~cm}$ and in $\triangle PQR, \angle P=90^{\circ}, PR=3 \mathrm{~cm}, QR=8$ $\mathrm{cm}$, then:

Option 1: $\triangle ABC \cong \triangle PQR$

Option 2: $ar(\triangle ABC)\neq ar(\triangle PQR)$

Option 3: $ar(\triangle ABC) \leq ar(\triangle PQR)$

Option 4: $ar(\triangle ABC)=ar(\triangle PQR)$

Question : The centroid of a $\triangle ABC$ is G. The area of $\triangle ABC$ is 60 cm². The area of $\triangle GBC$ is:

Option 1: 10 cm²

Option 2: 30 cm²

Option 3: 40 cm²

Option 4: 20 cm²