CAT Practice : Coordinate Geometry

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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).

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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.