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If k is an integer and 2 < k < 7, for how many different val
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02 Jun 2020, 01:48
02 Jun 2020, 01:48
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If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?
(A) one
(B) two
(C) three
(D) four
(E) five
(A) one
(B) two
(C) three
(D) four
(E) five
Re: If k is an integer and 2 < k < 7, for how many different val
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02 Jun 2020, 01:48
02 Jun 2020, 01:48
Expert Reply
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If k is an integer and 2 < k < 7, for how many different val
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02 Jun 2020, 04:51
02 Jun 2020, 04:51
1
Carcass wrote:
If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?
(A) one
(B) two
(C) three
(D) four
(E) five
(A) one
(B) two
(C) three
(D) four
(E) five
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
So, if a triangle has sides 2, 7 and k, we can write: 7 - 2 < k < 7 + 2
Simplify to get: 5 < k < 9
We're told that k is an INTEGER, and that 2 < k < 7.
So, the only possible value of k that satisfies the inequality 5 < k < 9 is k = 6
Answer: A
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