Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
D, and are the mid-point of sides CA and of then area area
D, \( E \) and \( F \) are the mid-point of sides \( B C \) CA and \( A B \) of \( \triangle A B C, \) then area \( \triangle A B C \) area \( \triangle \mathrm{DEF}= \)
- A. 4: 1
- B. 1: 4
- C. 2: 1
- D. 4: 3
Step-by-step solution
D, E, F are midpoints of sides BC, CA, AB respectively. Triangle DEF is the medial triangle, which is similar to triangle ABC with scale factor 1/2. The ratio of areas of similar triangles is the square of the scale factor, so area(DEF) = (1/2)^2 * area(ABC) = 1/4 * area(ABC). Hence area(ABC) : area(DEF) = 4:1.
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