Question

If $△$ ABC and $△$ BDE are equilateral triangles, where D is the mid-point of BC, find the ratio of areas of $△$ ABC and $△$ BDE.

Answer 1

Area of equilateral triangle $△ABC=\frac{\sqrt{3}{a}^2}{4}$

Area of equilateral triangle $△BDE=\frac{\sqrt{3}(\frac{a}{2}{)}^2}{4}=\frac{\sqrt{3}{a}^2}{16}$
Ratio of area of $△ABC$ and $△BDE$ $=\frac{\frac{\sqrt{3}{a}^2}{4}}{\frac{\sqrt{3}{a}^2}{16}}=4$

Hence the ratio of area of $△ABC$ and $△BDE=4$