This question was uploaded on 02/01/22 on social media accounts.
Solution 1:
Triangle ABC is 1/4 of the area of the square,
Let, the area of triangle ADE = 8A
Then, the area of triangle ABC = 15A
Now,
\[Fraction=\frac{2\times8}{4\times15}=\frac4{15}\]
Solution 2:
Let equal sides of the triangle have length 5 units.
\[\tan\alpha=\frac12\]
\[\Rightarrow\tan(45-\alpha)=\frac13\]
\[\Rightarrow\frac x4=\frac13\]
\[\Rightarrow x=\frac43\]
Blue Area:
\[\color{blue} {A=2\times\left(\frac12\times4\times\frac43\right)=\frac{16}3}\]
Square Area:
\[\color{red} {A=s^2=4^2+2^2=20}\]
Blue Fraction:
\[Fraction=\frac{\color{blue}{16/3}}{\color{red}{20}}=\frac4{15}\]
