Difference between revisions of "2023 AMC 10B Problems/Problem 17"
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| − | The | + | == 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); | ||
| + | |||
| + | </asy> | ||
| + | |||
| + | The diagonal of the box is | ||
| + | |||
| + | <cmath>\begin{align*} | ||
| + | \sqrt{a^+b^2+c^2}&= | ||
| + | \end{align*} | ||
| + | </cmath> | ||
| + | |||
| + | ~Technodoggo | ||
Revision as of 16:06, 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); [/asy]](http://latex.artofproblemsolving.com/9/6/7/967bc22c5ec30acc4ed2df3e5e4317082282b822.png)
The diagonal of the box is
~Technodoggo
