Question

ABC is an equilateral triangle of each side 4 cm and triangle PQR ia an equilateral triangle of each side 2 cm . find ratio of their areas ?

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{both}\mathrm{are}\mathrm{equilateral}\mathrm{triangle},\mathrm{So}\mathrm{measure}\mathrm{of}\mathrm{their}\mathrm{angles}\mathrm{is}\mathrm{equal}\mathrm{i}.\mathrm{e}.60° \\ \mathrm{By}\mathrm{AAA}\mathrm{similarity}\mathrm{criterion} \\ △\mathrm{ABC}~△\mathrm{PQR} \\ \mathrm{So}, \\ \frac{\mathrm{Area}\left(△\mathrm{ABC}\right)}{\mathrm{Area}\left(△\mathrm{PQR}\right)}={\left(\frac{\mathrm{AB}}{\mathrm{PQ}}\right)}^2={\left(\frac{4}{2}\right)}^2 \\ =4:1\mathrm{ANS}... \end{gathered}$$