Question : The areas of two similar triangles $\Delta ABC$ and $\Delta PQR$ are 36 sq. cm and 9 sq. cm, respectively. If $PQ$ = 4 cm, then what is the length of $AB$ (in cm)?
Option 1: 16 cm
Option 2: 12 cm
Option 3: 8 cm
Option 4: 6 cm
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Correct Answer: 8 cm
Solution :
Given: Two triangles $ABC$ and $PQR$ such that: $△ABC∼△PQR$.
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
So, $\frac{\text{area of }(\Delta ABC)}{\text{area of }(\Delta PQR)}=(\frac{AB}{PQ})^2$
⇒ $\frac{36}{9}=\frac{AB^2}{16}$
⇒ ${16} \times{4}={AB^2}$
⇒ $AB = 8$
Hence, the correct answer is 8 cm.
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