In the figure given below, P is a point inside the triangle ABC. Line segments DE, FG and
HI are drawn through P, parallel to the sides AB, BC and
CA respectively. The areas of the three triangles DPG, FPI
and EPH are 9, 16, and 25 respectively. What is the area
of the triangle ABC? (All the areas are in sq cm).
1) 100
2) 144
3) 150
4) 196
Answers
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2
Answer:
DE is parallel to AC
FG is parallel to BC
IH is parallel to AB
△PIE=49
△PDF=4
△PGH=9
△PGH≅△PIE
HP:PI=
9
:
49
=3:7
so, IP:IH=7:10
△PIE:△HIC=7
2
:10
2
area of △HIC=100
area of parallelogram PGCE=100−9−49=42
similarly,
are of parallelogram PIBF=(
4
+
49
)
2
−4−49
=81−53=28
are of parallelogram PDAH=(
4
+
9
)
2
−4−9
=25−13=12
are of △ABC=49+4+9+28+42+12=144
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