CAT Practice : Coordinate Geometry

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Triangles  Question 25
Find the ratio of the side of the square and the side of the triangle and you are through!!

Ratio of Areas

    Q.25: There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral △. What is the ratio of the area of the square to that of the equilateral triangle?

 

  • Correct Answer
    Choice (C).

Detailed Solution

Let side of square be ‘a’.
MN = LP = a
∠ABC = 60°
ML = a. BL = 𝑎 (Use some trigonometry for this)


PC =
BC = a + . We are done.
Area of square = a2
Area of equilateral triangle
= * (a + )2 = *a2 (√3 + 2)2

= *a2 (7 + 4√3)

Ratio =




Correct Answer: (C).



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.