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Omni-MATH / Let n be the answer to this problem. Suppose square ABCD has side-length 3. Then, congruent non-overlapping squares EHGF and IHJK of side-length (n)/(6) are drawn such that A,C, an…

Problem

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problem

Let nn be the answer to this problem. Suppose square ABCDABCD has side-length 3. Then, congruent non-overlapping squares EHGFEHGF and IHJKIHJK of side-length n6\frac{n}{6} are drawn such that A,CA, C, and HH are collinear, EE lies on BCBC and II lies on CDCD. Given that AJGAJG is an equilateral triangle, then the area of AJGAJG is a+bca+b\sqrt{c}, where a,b,ca, b, c are positive integers and cc is not divisible by the square of any prime. Find a+b+ca+b+c.
Plain-text mathematical notation (without MathML)
Let n be the answer to this problem. Suppose square ABCD has side-length 3. Then, congruent non-overlapping squares EHGF and IHJK of side-length (n)/(6) are drawn such that A,C, and H are collinear, E lies on BC and I lies on CD. Given that AJG is an equilateral triangle, then the area of AJG is a+b√(c), where a,b,c are positive integers and c is not divisible by the square of any prime. Find a+b+c.
Original LaTeX notation
Let $n$ be the answer to this problem. Suppose square $ABCD$ has side-length 3. Then, congruent non-overlapping squares $EHGF$ and $IHJK$ of side-length $\frac{n}{6}$ are drawn such that $A, C$, and $H$ are collinear, $E$ lies on $BC$ and $I$ lies on $CD$. Given that $AJG$ is an equilateral triangle, then the area of $AJG$ is $a+b\sqrt{c}$, where $a, b, c$ are positive integers and $c$ is not divisible by the square of any prime. Find $a+b+c$.

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Source and history

task_id
7aa52239-6098-5a56-a380-5a2f26265473
task_key
test--7aa52239-6098-5a56-a380-5a2f26265473
task_revision_id
1
config / split
/ test

Official source

initial import