# CAT 2017 Question Paper | Quants Slot 1

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

CAT Geometry is an important topic with lots of weightage in the CAT Exam. There are quite a few ways to find the area of the triangle. But which one to use when the lengths of the sides are given? It Looks like something heroic might work. But this question is beautiful because it tests a wonderful idea from the triangle. If you get this one idea correct, then you're through. Will you get this right or, you'll say, 'Damn! I missed it".

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. $$frac{500}{√3}$ 3. $\frac{275}{√3}$ 4. $\frac{250}{√3}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Geometry Given that from a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. Here GBC is the one third of the area of the triangle. We can join AG and GD which is the median. Each of the shaded triangle has the same area and therefore the remaining area is two-thirds of ABC The ratio of the sides are 8 : 5 : 7 Area of triangle = √$s(s−a)(s−b)(s−c))
where, semi perimeter (s) = $$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. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### 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? Mobile:$91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com