Question: Figure shows an equilateral triangle with side length equal to $1$ . Two squares of side length a and $2a$ placed side by side just fit inside the triangle as shown.
Find the exact value of $a$.
Its an Assessment question from edX course "A-Level Mathematics Course 1" and I am supposed to use skills that I learnt in Indices and surds,Inequalities and The Factor Theorem.
I have tried finding the height of triangle and then use similar triangles to find the right triangle length still No luck.
I am just looking for food for thought or very small hints thats all.