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
Explanation:
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
- $225\sqrt{3}$
- $\frac{500}{\sqrt{3}}$
- $\frac{275}{\sqrt{3}}$
- $\frac{250}{\sqrt{3}}$
Explanation:
The lengths are given as 40, 25 and 35.
The perimeter = 100
Semi-perimeter, s = 50
Area = $ \sqrt{50 × 10 × 25 × 15}$ = $250\sqrt{3}$
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 = $\frac{2}{3}× 250\sqrt{3}$ = $\frac{500}{\sqrt{3}}$
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