# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Geometry Questions | Question 16

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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√3
2. $$frac{500}{√3}$ 3. $\frac{275}{√3}$ 4. $\frac{250}{√3}$ ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Geometry Given that from a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. Here GBC is the one third of the area of the triangle. We can join AG and GD which is the median. Each of the shaded triangle has the same area and therefore the remaining area is two-thirds of ABC The ratio of the sides are 8 : 5 : 7 Area of triangle = √$s(s−a)(s−b)(s−c))
where, semi perimeter (s) = $$frac{8 + 5 + 7}{2}$ = 10 Area = √$10(10 − 8)(10 − 5)(10 − 7))
Area = √(10(2)(5)(3))
Area = 10√3
Area of ABC = 25 × 10 √3 (As 8 : 5 : 7 multiplied by 5 gives the sides of triangle ABC)
Therefore area of the remaining traingle = $$frac{2}{3}$ × 250√3 = $\frac{500}{√3}$ The question is "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 :" ##### Hence, the answer is $\frac{500}{√3}$ Choice B is the correct answer. ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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