2021 JMPSC Accuracy Problems/Problem 12

Problem

A rectangle with base $1$ and height $2$ is inscribed in an equilateral triangle. Another rectangle with height $1$ is also inscribed in the triangle. The base of the second rectangle can be written as a fully simplified fraction $\frac{a+b\sqrt{3}}{c}$ such that $gcd(a,b,c)=1.$ Find $a+b+c$ .

Solution

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2021 JMPSC Accuracy Problems/Problem 12

Problem

Solution