Problem 244

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Problem 244: (2016 AMC 12b, 10)

A quadrilateral has vertices $P(a,b)$, $Q(b,a)$, $R(-a, -b)$, and $S(-b, -a)$, where $a$ and $b$ are integers with $a>b>0$. The area of $PQRS$ is $16$. What is $a+b$? $\textbf{(A)}\ 4 \qquad$ $\textbf{(B)}\ 5 \qquad$ $\textbf{(C)}\ 6 \qquad$ $\textbf{(D)}\ 12 \qquad$ $\textbf{(E)}\ 13$

Solution

Exercise 244: Solution

A quadrilateral has vertices $P(2a,b)$, $Q(a,3b)$, $R(-2a,-b)$, and $S(-a,-3b)$, where $a$ and $b$ are integers with $a>b>0$. The area of $PQRS$ is $50$. What is $a+b$?

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