Question
Given $\triangle\text{ABC}\sim\triangle\text{PQR},\ \text{if}\ \frac{\text{AB}}{\text{PQ}}=\frac{1}{3},$ then find $\frac{\text{ar }\triangle\text{ABC}}{\text{ar}\ \triangle\text{PQR}}.$
✓
Answer
$\frac{\text{A}(\triangle\text{ABC})}{\text{A}(\triangle\text{PQR})}=\frac{\text{AB}^2}{\text{PQ}^2}$ (Ratio of area of similar triangle is equal to square of their proportional sides)$\frac{\text{A}(\triangle\text{ABC})}{\text{A}(\triangle\text{PQR})}=\Big(\frac{1}{3}\Big)^2=\frac{1}{9}$
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