Question

Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, then the length of the corresponding sides of the smaller triangle is __________.

Answer 1

We know that, the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$$\begin{gathered} \therefore \frac{\mathrm{Area}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Area}\mathrm{of}\mathrm{larger}\mathrm{triangle}}={\left(\frac{\mathrm{Length}\mathrm{of}\mathrm{corresponding}\mathrm{side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{\mathrm{Length}\mathrm{of}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{larger}\mathrm{triangle}}\right)}^2 \\ \Rightarrow \frac{36{\mathrm{cm}}^2}{100{\mathrm{cm}}^2}={\left(\frac{\mathrm{Length}\mathrm{of}\mathrm{corresponding}\mathrm{side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{20\mathrm{cm}}\right)}^2 \\ \Rightarrow \frac{\mathrm{Length}\mathrm{of}\mathrm{corresponding}\mathrm{side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}}{20\mathrm{cm}}=\sqrt{\frac{36}{100}}=\frac{6}{10} \\ \Rightarrow \mathrm{Length}\mathrm{of}\mathrm{corresponding}\mathrm{side}\mathrm{of}\mathrm{smaller}\mathrm{triangle}=\frac{3\times 20}{5}=12\mathrm{cm} \end{gathered}$$

Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, then the length of the corresponding sides of the smaller triangle is ___12 cm___.