CAT Practice : Geometry-Triangles

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Mathematicians love symmetry, question setters are nearly besotted with it. So, learn about symmetric figures well.

Equilateral triangle and square

    Q.6: 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?
    1. 12 : 12 + 7
    2. 24 : 24 + 7
    3. 18 : 12 + 15
    4. 6 : 6 + 5


  • Correct Answer
    Choice (A). 12 : 12 + 7

Explanatory Answer

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Detailed Solution

APQ is an equilateral △. As PQ is parallel to BC.
Let side of the square be ‘a’
AP = a = AQ
△QRC has angles 30 – 60 – 90.

QC = QR x

AC = AQ + QC
a +

Area of equilateral △

Ratio of area of square to that of equilateral △ is = =
Answer choice (a)

Correct Answer: 12 : 12 + 7

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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.