How many non-obtuse angled triangles with int...
How many non-obtuse angled triangles with integer sides are possible with 8 and 10 as 2 of its sides?

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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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