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CAT 2003 Slot 2 — QA Question 26

PolygonsEasy
Passage / Data

Answer the following question based on the information given below.

Consider three circular parks of equal size with centres at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3, as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.

The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t, and s, respectively. Then,

Answer & solution

  • A

    s > t > c

  • B

    c > t > s

  • c > s > t

  • D

    s > c > t

Solution

Let radius of the circle be r, a side of the equilateral triangle be a, and a side of the square be x.

The circumference/perimeter of the circle, triangle and square are equal. Hence,

2πr = 3a = 4x = k

∴r=k2π,a=k3, and x=k4

The areas of the circle, triangle and square are c, t, s respectively. Hence,

c=πr2=πk24π2=k24π,t=34a2=34×k29=k2123s=x2=k216∵1π>14>133∴c>s>t

Hence, option (c).

CAT 2003 Slot 2 QA Q26: The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the pe — Solution | TheCATExam