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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?

Manoj Kumar
Nov 10, 2020 |

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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)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,

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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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? for CAT 2022 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.

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? for CAT 2022 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.

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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.