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

  1. 144    
  2. 288    
  3. 72    
  4. none of these    

hintHint:

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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