Bodhee Prep-Online CAT Coaching | Online CAT Preparation | CAT Online Courses

15% OFF on all CAT Courses. Discount code: BODHEE015. Valid till 7th Feb Enroll Now

CAT 2020 Quant Question [Slot 2] with Solution 24

Question

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is

  1. \(\frac{{\sqrt 3 {s^2}}}{2}\)
  2. \(\frac{{{s^2}}}{{\sqrt 3 }}\)
  3. \(\frac{{2{s^2}}}{{\sqrt 3 }}\)
  4. \(\frac{{{s^2}}}{{2\sqrt 3 }}\)
Option: 2
Solution:

PD + PE + PF = s

Area of

\( = \frac{1}{2} \times AB \times PE + \frac{1}{2} \times BC \times PD + \frac{1}{2} \times AC \times PF\)

As \(AB = BC = CA,\) we've

\( = \frac{1}{2} \times AB(PD + PE + PF) = \frac{1}{2}AB \times s - (1)\)

Now \(\frac{{\sqrt 3 }}{4}A{B^2} = \frac{1}{2}AB \times s\)

\( \Rightarrow AB = \frac{2}{{\sqrt 3 }}s\)

Required value \( = \frac{1}{2} \times \frac{2}{{\sqrt 3 }} \times {s^2} = \frac{{{s^2}}}{{\sqrt 3 }}\)

CAT Online Course @ INR 11999 only

CAT 2020 Quant questions with Solutions

CAT Online Courses
FREE CAT prep Whatsapp Group