IMAS 2014–2015 — Junior — Round 2 Question 4

Question 4

The perimeter of an equilateral triangle is $a$ cm while the perimeter of a square is $b$ cm. If the area of the square is half the area of the triangle, what is the value of $\frac{a^2}{b^2}$?

$\frac{3\sqrt3}{8}$
$\frac{3\sqrt3}{4}$
$\frac{3\sqrt3}{2}$
$\frac{3\sqrt3}{3}$
$6\sqrt3$