Bodhee Prep-CAT Online Preparation

CAT 2017 [slot 1] Question with solution 16

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. $225\sqrt{3}$
  2. $\frac{500}{\sqrt{3}}$
  3. $\frac{275}{\sqrt{3}}$
  4. $\frac{250}{\sqrt{3}}$
Option: 2
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 = $\frac{2}{3}× 250\sqrt{3}$ = $\frac{500}{\sqrt{3}}$

Previous QuestionNext Question

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon