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The triangle shown above is Obtuse, where AC is the longest side and A
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30 Apr 2023, 23:10
30 Apr 2023, 23:10
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42% (01:37) correct
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The triangle shown above is Obtuse, where AC is the longest side and AB is the shortest side .What are all possible lengths of AB if k is a positive integer?
Indicate all that apply
3
4
5
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Re: The triangle shown above is Obtuse, where AC is the longest side and A
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28 May 2023, 00:44
28 May 2023, 00:44
Expert Reply
OE
Given that, ABC is an obtuse angled triangle, where AC is the longest side and AB is the
shortest side.
In a triangle,
(Difference of other two sides) < Any side of the triangle < (Sum of other two sides)
So,
3k – k < 10 < 3k + k
2k < 10 < 4k
Therefore, 2k < 10 and 10 < 4k
that is, k < 5 and 2.5 < k
Therefore, k lies between 2.5 and 5.
It is given that k is an integer,
Therefore, K can be 3 or 4.
If k = 3,
AC = 3k = 9
But it is given that AC is longest side
Hence, k cannot be 3.
If k = 4,
AB = 4 and AC = 3k = 12
This satisfies the statements given in the question.
The only value of k possible is 4.
Ans. (B)
Given that, ABC is an obtuse angled triangle, where AC is the longest side and AB is the
shortest side.
In a triangle,
(Difference of other two sides) < Any side of the triangle < (Sum of other two sides)
So,
3k – k < 10 < 3k + k
2k < 10 < 4k
Therefore, 2k < 10 and 10 < 4k
that is, k < 5 and 2.5 < k
Therefore, k lies between 2.5 and 5.
It is given that k is an integer,
Therefore, K can be 3 or 4.
If k = 3,
AC = 3k = 9
But it is given that AC is longest side
Hence, k cannot be 3.
If k = 4,
AB = 4 and AC = 3k = 12
This satisfies the statements given in the question.
The only value of k possible is 4.
Ans. (B)
Re: The triangle shown above is Obtuse, where AC is the longest side and A
[#permalink]
13 Jul 2023, 01:57
13 Jul 2023, 01:57
2
Pick the the number 4 what only satisfies the conditions about the triangle's sides- AC as the longest side and any two sides sum and difference are more and less respectively than the other side.
