Question : $\triangle P Q R$ is similar to $\triangle \mathrm{UVW}$. Perimeters of $\triangle \mathrm{PQR}$ and $\Delta \mathrm{UVW}$ are 120 cm and 240 cm respectively. If PQ = 30 cm, then what is the length of UV?
Option 1: 45 cm
Option 2: 75 cm
Option 3: 60 cm
Option 4: 90 cm
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Correct Answer: 60 cm
Solution : In similar triangles, the ratios of the respective sides are equal to the perimeter of the triangles. Using the concept ⇒ $\frac{\text{(perimeter of ΔPQR)}}{\text{(perimeter of ΔUVW)}} = \frac{\text{PQ}}{\text{UV}}$ ⇒ $\frac{120}{240} = \frac{30}{\text{UV}}$ ⇒ $\frac{1}{2} = \frac{30}{\text{UV}}$ ⇒ UV = 60 cm Hence, the correct answer is 60 cm.
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Question : $\triangle \mathrm{MNO}$ is similar to $\triangle \mathrm{STU}$. Perimeters of $\triangle \mathrm{MNO}$ and $\triangle \mathrm{STU}$ are 80 cm and 200 cm respectively. If ON = 25 cm, then what is the length of TU?
Option 1: 59 cm
Option 2: 61 cm
Option 3: 62.5 cm
Option 4: 60.5 cm
Question : $\triangle \mathrm {ABC}$ is similar to $\triangle \mathrm{PQR}$ and $\mathrm{PQ}=10 \mathrm{~cm}$. If the area of $\triangle \mathrm{ABC}$ is $32 \mathrm{~cm}^2$ and the area of $\triangle \mathrm{PQR}$ is $50 \mathrm{~cm}^2$, then the length of $A B$ (in $\mathrm{cm}$ ) is equal to:
Option 1: 10
Option 2: 4
Option 3: 6
Option 4: 8
Question : The perimeters of two similar triangles $\triangle$ABC and $\triangle$PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is:
Option 1: 15 cm
Option 2: 12 cm
Option 3: 14 cm
Option 4: 26 cm
Question : If in $\triangle PQR$ and $\triangle DEF, \angle P=52^{\circ}, \angle Q=74^{\circ}, \angle R=54^{\circ}, \angle D=54^{\circ}, \angle E=74^{\circ}$ and $\angle F=52^{\circ}$, then which of the following is correct?
Option 1: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$
Option 2: $\triangle \mathrm{RQP} \sim \triangle \mathrm{FED}$
Option 3: $\triangle \mathrm{PRQ} \sim \Delta \mathrm{FED}$
Option 4: $\triangle \mathrm{PQR} \sim \triangle \mathrm{DEF}$
Question : O is the incentre of the $\triangle \mathrm{PQR}$. If $\angle \mathrm{POR}=120°$, then what is the $\triangle \mathrm{PQR}$?
Option 1: 45°
Option 2: 60°
Option 3: 55°
Option 4: 48°
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