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
Correct Answer: 4.8 cm
Solution :
Given: $\triangle BAC\sim \triangle PQR$.
The area of $\triangle BAC$ and $\triangle PQR$ is 25 cm
2
and 36 cm
2
respectively.
BA = 4 cm
A similar triangle's area is proportional to the squares of the respective sides.
Let PQ be $x$ cm.
According to the question,
$\frac{\text{Area of $\triangle PQR$}}{\text{Area of $\triangle BAC$}}=\frac{(PQ)^2}{(BA)^2}$
⇒ $\frac{36}{25}=\frac{x^2}{4^2}$
⇒ $x^2=\frac{36\times 4^2}{25}$
⇒ $x=\frac{6\times 4}{5}=\frac{24}{5}$
⇒ $x=4.8$ cm
Hence, the correct answer is 4.8 cm.
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