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| A square of area <math>2</math> is inscribed in a square of area <math>3</math>, creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?
| | #redirect[[2023 AMC 12A Problems/Problem 9]] |
| [asy]
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| size(200);
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| defaultpen(linewidth(0.6pt)+fontsize(10pt));
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| real y = sqrt(3);
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| pair A,B,C,D,E,F,G,H;
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| A = (0,0);
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| B = (0,y);
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| C = (y,y);
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| D = (y,0);
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| E = ((y + 1)/2,y);
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| F = (y, (y - 1)/2);
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| G = ((y - 1)/2, 0);
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| H = (0,(y + 1)/2);
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| fill(H--B--E--cycle, gray);
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| draw(A--B--C--D--cycle);
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| draw(E--F--G--H--cycle);
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| [\asy]
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| <math>\textbf{(A) }\frac15\qquad\textbf{(B) }\frac14\qquad\textbf{(C) }2-\sqrt3\qquad\textbf{(D) }\sqrt3-\sqrt2\qquad\textbf{(E) }\sqrt2-1</math>
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