Compare a shaded triangle’s area with 54

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Quantitative Reasoning

Rectangle JKLM with side JK labeled 12, side KL labeled 9, and diagonal JL forming shaded right triangle JKL.

In the figure above, $JKLM$ is a rectangle. Quantity A: The area of the shaded region Quantity B: $54$

Compare Quantity A and Quantity B. Select one answer.

AQuantity A is greater.BQuantity B is greater.CThe two quantities are equal.DThe relationship cannot be determined from the information given.

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Answer: C (The two quantities are equal.)

Since $JKLM$ is a rectangle, sides $JK$ and $KL$ are perpendicular. Therefore, the shaded region is a right triangle with base $12$ and height $9$ . Its area is $(\frac{1}{2})(12)(9) = 54$ . Thus, the two quantities are equal.

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Quantitative Reasoning

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