2023 AMC 10A Problems/Problem 17

Let $ABCD$ be a rectangle with $AB = 30$ and $BC = 28$ . Point $P$ and $Q$ lie on $\overline{BC}$ and $\overline{CD}$ respectively so that all sides of $\triangle{ABP}, \triangle{PCQ},$ and $\triangle{QDA}$ have integer lengths. What is the perimeter of $\triangle{APQ}$ ?

$\text{A) } 84 \qquad \text{B) } 86 \qquad \text{C) } 88 \qquad \text{D) } 90 \qquad \text{E) } 92$

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2023 AMC 10A Problems/Problem 17

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