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Question

# Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.

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Solution

## According to theorem of areas of similar triangles "When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides". $\therefore \frac{\mathrm{Area}\mathrm{of}\mathrm{bigger}\mathrm{triangle}}{\mathrm{Area}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}=\frac{225}{81}\phantom{\rule{0ex}{0ex}}⇒\frac{{\left(\mathrm{Side}\mathrm{of}\mathrm{bigger}\mathrm{triangle}\right)}^{2}}{{\left(\mathrm{Side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}\right)}^{2}}=\frac{{15}^{2}}{{9}^{2}}\phantom{\rule{0ex}{0ex}}⇒\frac{\mathrm{Side}\mathrm{of}\mathrm{bigger}\mathrm{triangle}}{\mathrm{Side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}=\frac{15}{9}$​ $⇒\mathrm{Side}\mathrm{of}\mathrm{bigger}\mathrm{triangle}=\frac{15}{9}×\mathrm{Side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}\phantom{\rule{0ex}{0ex}}⇒\mathrm{Side}\mathrm{of}\mathrm{bigger}\mathrm{triangle}=\frac{15}{9}×12\phantom{\rule{0ex}{0ex}}=20$ Hence, the corresponding side of the bigger triangle is 20.

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