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PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of Δ PXQ and ARXS is
  • a)
    6:1
  • b)
    3:1
  • c)
    9:1
  • d)
    7:1
Correct answer is option 'C'. Can you explain this answer?
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PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The...
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PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The...
Given: PQRS is a trapezium with PQ || RS and PQ = 3RS. The diagonals of the trapezium intersect at X.

To find: The ratio of the areas of triangles PXQ and RXS.

Solution:

Step 1: Draw a rough figure of the trapezium PQRS and mark the given information.

Step 2: Draw the diagonals PR and QS which intersect at X.

Step 3: Divide the trapezium into two triangles PXQ and RXS by drawing a line parallel to PQ through point S.

Step 4: Now we need to find the ratio of the areas of triangles PXQ and RXS.

Step 5: Let the height of the trapezium be h.

Step 6: We know that PQ = 3RS. Let RS = x. Then PQ = 3x.

Step 7: The area of trapezium PQRS = (1/2)h(PQ + RS) = (1/2)h(3x + x) = 2hx.

Step 8: Using the area of a triangle formula, the area of triangle RXS = (1/2)xh and the area of triangle PXQ = (1/2)(3x)h = (3/2)xh.

Step 9: Therefore, the ratio of the areas of triangles PXQ and RXS = (3/2)xh / (1/2)xh = 3:1.

Step 10: Hence, the correct option is (c) 9:1.

Final Answer: The ratio of the areas of triangles PXQ and RXS is 9:1.
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PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of Δ PXQ and ARXS isa)6:1b)3:1c)9:1d)7:1Correct answer is option 'C'. Can you explain this answer?
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PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of Δ PXQ and ARXS isa)6:1b)3:1c)9:1d)7:1Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of Δ PXQ and ARXS isa)6:1b)3:1c)9:1d)7:1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQRS is trapezium, in which PQ is parallel to RS, and PQ = 3 (RS). The diagonal of the trapezium intersect each other at X, then the ratio of Δ PXQ and ARXS isa)6:1b)3:1c)9:1d)7:1Correct answer is option 'C'. Can you explain this answer?.
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