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KVPY2017MathematicsProperties of Triangles

Let X, Y, Z be respectively the areas of a regular pentagon, regular hexagon and regular heptagon which are inscribed in a circle of radius 1 . Then

Options

  1. Ax 5 < Y 6 < Z 7 and X < Y < Z
  2. Bx 5 Y > Z
  3. Cx 5 > Y 6 > Z 7 and X > Y > Z ,
  4. Dx 5 > Y 6 > Z 7 and X < Y < Z

Correct answer

D. x 5 > Y 6 > Z 7 and X < Y < Z

Step-by-step solution

Area of Pentagon =5 1 2 72^ =2.377= x Area of hexagon =6 1 2 60^ =3 3 2 =2.598= y Area of heptagon =7 1 2 360^ 7 =2.73= z

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