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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