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2021 April MIMC 10 Problems/Problem 6

Revision as of 22:01, 20 April 2021 by Cellsecret (talk | contribs) (Created page with "A worker cuts a piece of wire into two pieces. The two pieces, <math>A</math> and <math>B</math>, enclose an equilateral triangle and a square with equal area, respectively. T...")
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A worker cuts a piece of wire into two pieces. The two pieces, $A$ and $B$, enclose an equilateral triangle and a square with equal area, respectively. The ratio of the length of $B$ to the length of $A$ can be expressed as $a\sqrt[b]{c}:d$ in the simplest form. Find $a+b+c+d$.

$\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~12 \qquad\textbf{(D)} ~14 \qquad\textbf{(E)} ~15$

Solution

To be Released on April 26th.

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