In the figure above, squares PQRV and VRST have sides of length 6 cm.Quantity A: The area of the shaded region PQS.Quantity B: 36cm2
Correct answer: C. The two quantities are equal.
- A. Quantity A is greater.
- B. Quantity B is greater.
- C. The two quantities are equal.
- D. The relationship cannot be determined from the information given.
Explanation
To find the area of the shaded region PQS, note that PQS forms a right triangle with base PQ and height QS. Since squares PQRV and VRST have sides of 6 cm, the diagonal PQ (or QS) is 6√2 cm, but for the triangle's area calculation, we consider the base and height along the sides of the square. The area of triangle PQS is 1/2 * base * height = 1/2 * 12 * 6 = 36 cm2, which equals Quantity B. Therefore, Quantity A and Quantity B are equal.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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