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An integral triangle is a triangle all of whose sides have integer lengths. It is given that one side of an integral triangle is four times the second side and that the length of the third side is 18. Which is the integer nearest to the maximum area possible for this triangle?
  • a)
    33
  • b)
    38
  • c)
    48
  • d)
    43
Correct answer is option 'D'. Can you explain this answer?

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Manoj Kumar
Nov 10, 2020
Related An integral triangle is a triangle all of whose sides have integer lengths. It is given that one side of an integral triangle is four times the second side and that the length of the third side is 18. Which is the integer nearest to the maximum area possible for this triangle?a)33b)38c)48d)43Correct answer is option 'D'. Can you explain this answer?
Let the smaller side be x then the other side is 4x and the area of the triangle be ‘a’.
Using triangle inequality, we get,
As it is an integral triangle only possible values for x are 4 and 5. Maximum length of sides is 5, 20 and 18.

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Let the smaller side be x then the other side is 4x and the area of the triangle be a.Using triangle inequality, we get,As it is an integral triangle only possible values for x are 4 and 5. Maximum length of sides is 5, 20 and 18.