MBApyq

Area Remaining After Centroid Cut

CAT 2017 Slot 1 · Quantitative Ability · Hard · Geometry

This is a hard Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Geometry. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2017 Slot 1 questionsMore Geometry questionsAll CAT QA

From a triangle ABCABC with sides of lengths 40 ft40\text{ ft}, 25 ft25\text{ ft} and 35 ft35\text{ ft}, a triangular portion GBCGBC is cut off where GG is the centroid of ABCABC. The area, in sq ft, of the remaining portion of triangle ABCABC is:

  1. A.

    2253225\sqrt{3}

  2. B.

    5003\frac{500}{\sqrt{3}}

  3. C.

    2753\frac{275}{\sqrt{3}}

  4. D.

    2503\frac{250}{\sqrt{3}}

Answer

B

Explanation

Centroid divides triangle into three equal area triangles: Area(GBC)=13Area(ABC)\text{Area}(GBC) = \frac{1}{3} \text{Area}(ABC). Remaining area = 23Area(ABC)\frac{2}{3} \text{Area}(ABC). Using Heron's formula for a=40,b=25,c=35a=40, b=25, c=35: s=40+25+352=50s = \frac{40+25+35}{2} = 50. Area(ABC)=50(10)(25)(15)=187500=2503\text{Area}(ABC) = \sqrt{50(10)(25)(15)} = \sqrt{187500} = 250\sqrt{3}. Remaining area = 23×2503=50033=5003\frac{2}{3} \times 250\sqrt{3} = \frac{500\sqrt{3}}{3} = \frac{500}{\sqrt{3}}.

Related Geometry questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace