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KVPY2020MathematicsProperties of Triangles

Six consecutive sides of an equiangular octagon are 6 ,   9 ,   8 ,   7 ,   10 ,   5 in that order. The integer nearest to the sum of the remaining two sides is

Options

  1. A17
  2. B18
  3. C19
  4. D20

Correct answer

B. 18

Step-by-step solution

Let ABCDEFGH be the equiangular octagon as shown P Q = S R ⇒ y 2 + 6 + 9 2 = 5 2 + 10 + 7 2 ⇒ y = 3 + 4 2 Also: P S = Q R ⇒ y 2 + x + 5 2 = 9 2 + 8 + 7 2 ⇒ x = 4 + 4 2 ∴ x + y = 7 + 8 2 = 18 . 313 ∴ Nearest integer = 18 18

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