Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
In a triangle a line is drawn parallel to , points , Q being on and respectively
In a triangle \( A B C, \) a line \( P Q \) is drawn parallel to \( B C \), points \( P \), Q being on \( A B \) and \( A C \) respectively. If \( A B=3 A P \) then what is the ratio of the area of triangle \( A P Q \) to the area of triangle \( A B C ? \)
- A. 1: 3
- B. 1: 5
- C. 1: 7
- D. 1: 9
Step-by-step solution
Since PQ is parallel to BC, triangles APQ and ABC are similar. Given AB = 3 AP, so AP/AB = 1/3. The ratio of areas of similar triangles is the square of the ratio of corresponding sides, so (AP/AB)^2 = (1/3)^2 = 1/9. Hence the required ratio is 1:9.
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