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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

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 Correct Answer 500/√3

Calculation:

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⇒ In triangle ABC sides of triangle 40 ft, 25 ft, and 35 ft.

⇒ A triangular portion GBC cut off where G is the centroid

⇒ We join AG and GD which is the median. 

⇒ Each triangle have the same area So the remaining area is (2/3)rd of ΔABC

⇒ The ratio of the sides of the triangle = 8 : 5 : 7

⇒ The semiperimeter 's' = (8 + 5 + 7)/2 = 10

⇒ The area of triangle = √{s (s - a) (s - b) (s - c)}

⇒ 10 √3

⇒ The area of trialgle ABC = 25 × 10 √3 = 250 √3

⇒ The area of the remaining triangle = (2/3) × 250 √3 = 500/√3

∴ The required result will be 500/√3.

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