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
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Correct Answer: 8
Solution :
If $\triangle \mathrm{A B C}$ is similar to $\triangle \mathrm{PQR}$
⇒ $\frac{\text{Ares of triangle ABC}}{AB^2}=\frac{\text{Area of triangle PQR}}{PQ^2}$
⇒ $\frac{32}{AB^2}=\frac{50}{10^2}$
⇒ $AB^2=\frac{32}{50}\times 100$
⇒ $AB^2=64$ cm
⇒ $AB=\sqrt{64}=8$ cm
Hence, the correct answer is 8 cm.
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