Maths-
General
Easy
Question
P is a point inside the triangle ABC. Lines are drawn through P parallel to the sides of the triangle. The areas of the three resulting triangles with a vertex at P are 4, 9 and 49, then the area of ABC is
- 144
- 288
- 72
- none of these
Hint:
find the similar triangles and apply the rules of similarity in triangles to find the areas of the parallelograms.
The correct answer is: 144
144
the following triangles are similar
PQ1R1 and PQ2R2
Therefore, ratio of sides = √9: √49
= 3: 7
Q1P: Q1R2 = 7:10
Ratio of area of triangles PQ1R1: R2Q1C= 49 : 100
Area of parallelogram PQ2CR1 = 100-49-9=42
Similarly, area of parallelogram PQ1BR3= 81-4-49=28
area of parallelogram PQ2AR2 = 25-4-9=12
Area of triangle ABC = 49+4+9+28+42+12 = 144
ratio of sides of similar triangles = square root of the ratio of areas of the triangles. the converse is also true.
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