Question

From a triangle $ABC$ with sides of lengths $40	ext{ ft}$, $25	ext{ ft}$ and $35	ext{ ft}$, 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:

Accepted Answer

B. Centroid divides triangle into three equal area triangles: $	ext{Area}(GBC) = \frac{1}{3} 	ext{Area}(ABC)$. Remaining area = $\frac{2}{3} 	ext{Area}(ABC)$. Using Heron's formula for $a=40, b=25, c=35$: $s = \frac{40+25+35}{2} = 50$. $	ext{Area}(ABC) = \sqrt{50(10)(25)(15)} = \sqrt{187500} = 250\sqrt{3}$. Remaining area = $\frac{2}{3} 	imes 250\sqrt{3} = \frac{500\sqrt{3}}{3} = \frac{500}{\sqrt{3}}$.

Area Remaining After Centroid Cut

Explanation

Practise this under exam conditions