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− | == Solution ==
| + | #redirect[[2023 AMC 12B Problems/Problem 13]] |
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− | <asy>
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− | import geometry;
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− | pair A = (-3, 4);
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− | pair B = (-3, 5);
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− | pair C = (-1, 4);
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− | pair D = (-1, 5);
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− | pair AA = (0, 0);
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− | pair BB = (0, 1);
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− | pair CC = (2, 0);
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− | pair DD = (2, 1);
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− | draw(D--AA,dashed);
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− | draw(A--B);
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− | draw(A--C);
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− | draw(B--D);
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− | draw(C--D);
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− | draw(A--AA);
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− | draw(B--BB);
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− | draw(C--CC);
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− | draw(D--DD);
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− | // Dotted vertices | |
− | dot(A); dot(B); dot(C); dot(D);
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− | dot(AA); dot(BB); dot(CC); dot(DD);
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− | draw(AA--BB);
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− | draw(AA--CC);
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− | draw(BB--DD);
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− | draw(CC--DD);
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− | label("a",midpoint(D--DD),E);
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− | label("b",midpoint(CC--DD),E);
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− | label("c",midpoint(AA--CC),S);
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− | </asy>
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− | The diagonal of the box is
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− | <cmath>\begin{align*}
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− | \sqrt{a^2+b^2+c^2}&=\sqrt{(a+b+c)^2-2(ab+bc+ca)}\\
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− | &=\sqrt{(\dfrac{13}{4})^2-\dfrac{11}{2}}\\
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− | &=\dfrac{9}{4}
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− | \end{align*}
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− | </cmath>
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− | ~Technodoggo
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