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How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?
    Correct answer is '7'. Can you explain this answer?

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    EduRev CAT
    Dec 13, 2021
    Related How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?Correct answer is '7'. Can you explain this answer?
    Let the third side c be the smallest of the 3. In that case 10 - 8 < c, c>2
    c can take 3. 
    Let the side c be the largest side,  in that case, 10 + 8 > c, c<18
    c can take 17.
    So it can also take all values in between.
    If a triangle is obtuse-angled, then a2 + b2 < c2 
    So, all possible triangles are
    3,8,10 - obtuse
    4,8,10 - obtuse
    5,8,10 - obtuse
    6,8,10
    7,8,10
    8,8,10
    9,8,10
    10,8,10
    11,8,10
    12,8,10
    13,8,10 - obtuse
    14,8,10 - obtuse
    15,8,10 - obtuse
    16,8,10 - obtuse
    17,8,10 - obtuse
    So, 7 non-obtuse triangles are possible.

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    How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?Correct answer is '7'. 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 How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?Correct answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?Correct answer is '7'. Can you explain this answer?.
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    Let the third side c be the smallest of the 3. In that case 10 - 8 < c, c>2c can take 3.Let the side c be the largest side, in that case, 10 + 8 > c, c<18c can take 17.So it can also take all values in between.If a triangle is obtuse-angled, then a2 + b2 < c2So, all possible triangles are3,8,10 - obtuse4,8,10 - obtuse5,8,10 - obtuse6,8,107,8,108,8,109,8,1010,8,1011,8,1012,8,1013,8,10 - obtuse14,8,10 - obtuse15,8,10 - obtuse16,8,10 - obtuse17,8,10 - obtuseSo, 7 non-obtuse triangles are possible.