CAT 2017 Question Paper (Shift-1) Question 82

Question 82

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

Solution

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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Comments

Apoorv Sahai

3 years, 7 months ago

Can you please explain how the area is 2/3rd of the triangle ? and how did 2:1 ratio help us reach this conclusion ?

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