In ΔABC, P is a point on BC such that BP : PC = 4 : 5 and Q is the midpoint of BP, then ar(ΔABQ) : ar(ΔABC) is equal to?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2 : 9
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Concept |
Understanding |
Application |
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If heights of 2 triangles are same: Ratio of areas of triangles = Ratio of Base of triangles |
Given: BP : PC = 4 : 5 Hence, BC = 4x + 5x = 9x
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Since Q is the midpoint of BP: BQ = BP/2 = 4x/2 = 2x Here, the heights of triangles ABQ and ABC are same: ar ΔABQ : ar ΔABC = BQ : BC ⇒ ar ΔABQ : ar ΔABC = 2 : 9 |