What is the ratio of the area of the quadrilateral PQNM to the area of the quadrilateral RSNM?
Consider the following for the next two (02) items that follow:<br>Let two parallel line segments PQ=5 cm and RS=3 cm be perpendicular to a horizontal line AB, as shown in the figure given below. The point of intersection of PS and QR is M and MN is perpendicular to QS.
- A. \frac{200}{117}
- B. \frac{212}{117}
- C. \frac{275}{117} ✓
- D. \frac{250}{117}
Correct Answer: C. \frac{275}{117}
Explanation
The base QS is divided by N in the exact ratio of the pole heights, meaning QN:NS = 5:3. Both quadrilaterals are trapezoids. The ratio of their areas is \frac{\frac{1}{2}(PQ+MN) \times QN}{\frac{1}{2}(RS+MN) \times NS}. Substituting the lengths gives \frac{(5 + 15/8) \times 5}{(3 + 15/8) \times 3} = \frac{275}{117}.
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