Dare2solve | Fraction of area of small triangle inside an isosceles triangle to the area of large triangle

This question was uploaded on 15/11/21 on social media accounts.

Solutions:

By two similar triangles:

\[\frac a{2a} = \frac{2a}h\]

\[\Rightarrow h = 4a\]

Blue area:

\[A_1=\frac{(a)(2a)}{2}=a^2\]

Large triangle area:

\[A_2=2\times\frac{(2a)(4a)}{2}=8a^2\]

Fraction:

\[Ratio=\frac{A_1}{A_2}=\frac{a^2}{8a^2}=\frac18\]