Difference between revisions of "2023 AMC 10B Problems/Problem 17"
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Technodoggo (talk | contribs) (→Solution) |
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draw(CC--DD); | draw(CC--DD); | ||
| + | |||
| + | label("a",midpoint(D--DD),E); | ||
| + | label("b",midpoint(CC--DD),E); | ||
| + | label("c",midpoint(AA--CC),S); | ||
</asy> | </asy> | ||
| Line 48: | Line 52: | ||
<cmath>\begin{align*} | <cmath>\begin{align*} | ||
| − | \sqrt{a^+b^2+c^2}&= | + | \sqrt{a^2+b^2+c^2}&=\sqrt{(a+b+c)^2-2(ab+bc+ca)}\\ |
| + | &=\sqrt{(\dfrac{13}{4})^2-\dfrac{11}{2}}\\ | ||
| + | &=\dfrac{9}{4} | ||
\end{align*} | \end{align*} | ||
</cmath> | </cmath> | ||
~Technodoggo | ~Technodoggo | ||
Revision as of 15:09, 15 November 2023
Solution
![[asy] import geometry; pair A = (-3, 4); pair B = (-3, 5); pair C = (-1, 4); pair D = (-1, 5); pair AA = (0, 0); pair BB = (0, 1); pair CC = (2, 0); pair DD = (2, 1); draw(D--AA,dashed); draw(A--B); draw(A--C); draw(B--D); draw(C--D); draw(A--AA); draw(B--BB); draw(C--CC); draw(D--DD); // Dotted vertices dot(A); dot(B); dot(C); dot(D); dot(AA); dot(BB); dot(CC); dot(DD); draw(AA--BB); draw(AA--CC); draw(BB--DD); draw(CC--DD); label("a",midpoint(D--DD),E); label("b",midpoint(CC--DD),E); label("c",midpoint(AA--CC),S); [/asy]](http://latex.artofproblemsolving.com/4/e/4/4e4fcd74b454deedf3f32aa14c6c0e53b07d3002.png)
The diagonal of the box is
~Technodoggo
