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Question: Answered & Verified by Expert
P is a point inside the ΔABC. Three straight lines parallel to AB, BC and AC are drawn which divides the triangle into six regions. If the area of three triangles formed in these regions are 9,16 and 25 square units, then the area (in sq. units) of ΔABC is
MathematicsStraight LinesJEE Main
Options:
  • A 81 
  • B 256 
  • C 144
  • D 64
Solution:
1561 Upvotes Verified Answer
The correct answer is: 144


ΔABCΔTUPΔPDEΔSPR all are similar
ratio of areas =ratio of sides2
Let, PT=α=AS
SRPT=45SR=4α5
PEPT=35PE=3α5
AC=AS+SR+RC
=α+4α5+3α5
=12α5
arΔABCarΔPDE=AC2PE2=122·α252·32α252
Hence, arΔABC=16arΔPDE=144 sq. units

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