1. From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
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By: anil on 05 May 2019 02.29 am
The lengths are given as 40, 25 and 35. The perimeter = 100 Semi-perimeter, s = 50 Area = $$ sqrt{50 * 10 * 25 * 15}$$ = $$250sqrt{3}$$ The triangle formed by the centroid and two vertices is removed.
Since the cenroid divides the median in the ratio 2 : 1 The remaining area will be two-thirds the area of the original triangle. Remaining area = $$frac{2}{3} * 250sqrt{3}$$ = $$frac{500}{sqrt{3}}$$
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Since the cenroid divides the median in the ratio 2 : 1 The remaining area will be two-thirds the area of the original triangle. Remaining area = $$frac{2}{3} * 250sqrt{3}$$ = $$frac{500}{sqrt{3}}$$