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Let $A=(0,1),$ $B=(2,5),$ $C=(5,2),$ and $D=(7,0).$ A figure is created by connecting $A$ to $B,$ $B$ to $C,$ $C$ to $D,$ and $D$ to $A.$ The perimeter of $ABCD$ can be expressed in the form $a\sqrt2+b\sqrt{5}$ with $a$ and $b$ integers. What is the sum of $a$ and $b$?

 Jul 24, 2020
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https://artofproblemsolving.com/wiki/index.php/2013_AMC_10A_Problems/Problem_18

 Jul 24, 2020

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