Question : In the given figure, the triangle PQR is right-angled at Q. If PQ = 35 cm and QS = 28 cm and a semicircle passes from the point QRS, then what is the value (in cm) of SR?

Option 1: 35.33

Option 2: 37.33

Option 3: 41.33

Option 4: 43.33

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 : 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 : $\triangle BAC\sim \triangle PQR$. 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 : 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 : PQR is an equilateral triangle and the centroid of triangle PQR is point A. If the side of the triangle is 12 cm, then what is the length of PA?

Option 1: $4 \sqrt{3}$ cm

Option 2: $8 \sqrt{3}$ cm

Option 3: $2 \sqrt{3}$ cm

Option 4: $\sqrt{3}$ cm