For a triangle ABC, D. E. F are the mid-points of its sides. If ΔABC = 24 sq. units then ΔDEF is ?->(Show Answer!)

1. For a triangle ABC, D. E. F are the mid-points of its sides. If ΔABC = 24 sq. units then ΔDEF is

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By: anil on 05 May 2019 01.55 am

Property : The line joining the mid points of two sides of a triangle is parallel to the third side and half of it. => $$DF = frac{1}{2}BC$$ => $$frac{DF}{BC} = frac{1}{2}$$ Similarly, $$frac{DE}{AC} = frac{1}{2}$$ and $$frac{EF}{AB} = frac{1}{2}$$ Hence, $$ riangle$$ ABC $$sim$$ $$ riangle$$ DEF Property : The ratio of areas of two similar triangles is equal to the square of ratio of their corresponding sides. => $$frac{ar( riangle DEF)}{ar( riangle ABC)} = frac{DF^2}{BC^2}$$ => $$frac{ar( riangle DEF)}{24} = frac{1}{4}$$ => $$ar( riangle DEF)$$ = 6 sq. units

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