This question was uploaded on 24/01/22 on social media accounts.
Question is from @mathematics.azerbaijan from Instagram.
Solution:
Blue and green are equilateral triangles.
Yellow triangles are similar.
\[\color{black} {\Rightarrow \frac y3 = \frac {x+y}5 = \frac7{5+3}}\]
\[\color{black} {\Rightarrow x=\frac{16}7}\]
\[\color{blue} {A_{Blue}=\frac{\sqrt3}4\left(\frac{16}7\right)^2=\frac{64\sqrt3}{49}}\]
\[\color{red} {A_{Total}=\frac{\sqrt3}4\left(8\right)^2=16\sqrt3}\]
Blue Fraction:
\[\color{black} {\frac{\color{blue}{A_{Blue}}}{\color{red}{A_{Total}}}=\frac{\color{blue}{64\sqrt3/49}}{\color{red}{16\sqrt3}}=\frac{4}{49}}\]
