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Question 16 : 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 :

1. 225√3
2. \\frac{500}{√3})
3. \\frac{275}{√3})
4. \\frac{250}{√3})

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Geometry

Given that 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. Here GBC is the one third of the area of the triangle.
We can join AG and GD which is the median. Each of the shaded triangle has the same area and therefore the remaining area is two-thirds of ABC
The ratio of the sides are 8 : 5 : 7
Area of triangle = √(s(s−a)(s−b)(s−c))
where, semi perimeter (s) = \\frac{8 + 5 + 7}{2}) = 10
Area = √(10(10 − 8)(10 − 5)(10 − 7))
Area = √(10(2)(5)(3))
Area = 10√3
Area of ABC = 25 × 10 √3 (As 8 : 5 : 7 multiplied by 5 gives the sides of triangle ABC)
Therefore area of the remaining traingle = \\frac{2}{3}) × 250√3 = \\frac{500}{√3})

The question 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 :"

Hence, the answer is \\frac{500}{√3})

Choice B is the correct answer.