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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
33% (01:12) correct
67%
(02:28)
wrong
based on 18
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How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Are You Up For the Challenge: 700 Level Questions
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Are You Up For the Challenge: 700 Level Questions
Let the three sides be a, b & c. As the triangles cannot be equilateral nor isosceles \(a<b<c\) and their sum must be less than 15. One rule for triangles that is helpful here is that the sum of any two sides must be greater than the third.
Using this one can find triplets that add up to less than 15, and where any two of the numbers summed will yield a number greater than the third:
\(2, 3, 4\)
\(2, 4, 5\)
\(2, 5, 6\)
\(3, 4, 5\)
\(3, 4, 6\)
\(3, 5, 6\)
6 in total. However, as no right-angle triangles are allowed, one cannot include \(3, 4, 5\) as it is a special right-angle triangle.
Answer C, 5.
Using this one can find triplets that add up to less than 15, and where any two of the numbers summed will yield a number greater than the third:
\(2, 3, 4\)
\(2, 4, 5\)
\(2, 5, 6\)
\(3, 4, 5\)
\(3, 4, 6\)
\(3, 5, 6\)
6 in total. However, as no right-angle triangles are allowed, one cannot include \(3, 4, 5\) as it is a special right-angle triangle.
Answer C, 5.
02 Jun 2022, 03:57
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Nidzo
The answer will be 4, not 5.
3-4-7 is not a feasible combination since it violates the property of a triangle. Sum of 2 sides should be greater than the 3rd side. Since 3+4 = 7 which is not > 7, this is not possible.
The answer will be 4, not 5.
3-4-7 is not a feasible combination since it violates the property of a triangle. Sum of 2 sides should be greater than the 3rd side. Since 3+4 = 7 which is not > 7, this is not possible.
