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16 Sep 2025, 08:43
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Difficulty:
65%
(hard)
Question Stats:
16% (01:21) correct
83% (01:18) wrong based on 6 sessions
History
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The lengths of three sides of a triangle are 12, 17, and x. The perimeter of the triangle could be which of the following?
Indicate all that apply.
A. 28
B. 34
C. 40
D. 57
E. 60
Indicate all that apply.
A. 28
B. 34
C. 40
D. 57
E. 60
28 Sep 2025, 04:05
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Official Explanation
The triangle inequality states that in a triangle, the sum of any two of the side lengths is always greater than the length of any one. Equivalently, any one side length in a triangle must be less than the sum of the other two, but greater than the difference of the other two side lengths. Here, \(17 – 12 < x < 17 + 12,\) or \(5 < x < 29.\) Then the sum of the triangle’s three side length, its perimeter, will be greater than 5 + 12 + 17 but less than 29 + 12 + 17. This means 34 < perimeter <58. Choices (C) and (D) satisfy this.
Answer: C,D
The triangle inequality states that in a triangle, the sum of any two of the side lengths is always greater than the length of any one. Equivalently, any one side length in a triangle must be less than the sum of the other two, but greater than the difference of the other two side lengths. Here, \(17 – 12 < x < 17 + 12,\) or \(5 < x < 29.\) Then the sum of the triangle’s three side length, its perimeter, will be greater than 5 + 12 + 17 but less than 29 + 12 + 17. This means 34 < perimeter <58. Choices (C) and (D) satisfy this.
Answer: C,D
