Problem 274

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Problem 274: (2015 AMC 10a, 24; 2015 AMC12A, 19)

For some positive integers $p$, there is a quadrilateral $ABCD$ with positive integer side lengths, perimeter $p$, right angles at $B$ and $C$, $AB=2$, and $CD=AD$. How many different values of $p<2015$ are possible? $\textbf{(A) }30\qquad$ $\textbf{(B) }31\qquad$ $\textbf{(C) }61\qquad$ $\textbf{(D) }62\qquad$ $\textbf{(E) }63$

Solution

Exercise 274: Solution

For some positive integers $p$, there is a quadrilateral $ABCD$ with positive integer side lengths, perimeter $p$, right angles at $B$ and $C$, $AB=3$, and $CD=AD$. How many different values of $p<2015$ are possible?

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