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CAT 2020 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Quants Questions | Question 2

Geometry is the second most important topic of the Quantitative Ability section of the CAT exam. Acing this topic requires you to understand the basic concepts and practice a lot of questions levelling up your preparation game. One of the important things to cover for this are the CAT previous year paper that help you get a hang of the type and pattern of the questions the CAT Question Paper throws at you. Don't wait for you to complete your syllabus before diving into these actual CAT Exam questions. Try this geometry question taken from CAT 2020 Question paper right now without having a look at the solution provided and see where you stand.

Question 2 : From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is 's'. Then the area of the triangle is

  1. \\frac{s^{2}}{2√3})
  2. \\frac{2s^{2}}{√3})
  3. \\frac{s^{2}}{√3})
  4. \\frac{√3s^{2}}{2})

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Explanatory Answer

Right Triangle
From any point on a equilateral triangle, if we draw three perpendiculars on other sides
Those three perpendicular will add up to = Altitude of an equilateral triangle
We take the point to be A, and try to draw 3 perpendiculars (Can draw only one)
And is same as altitude of the equilateral triangle
So, s = \\frac{√3}{2}) a --> a = \\frac{2s}{√3})
By substituting the value in Area of an equilateral triangle \\frac{√3}{4})a2
\\frac{√3}{4}) × (\\frac{2s}{√3}))2= \\frac{s^{2}}{√3})


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

Hence, the answer is, "\\frac{s^{2}}{√3})"

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