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What is the possible value if perimeter of a triangle is 42 cm and it's largest side is a fundamental number?
Wiki User
∙ 7y ago
I am not sure what you mean by a "fundamental" number (I've never heard of that term being used with reference to the numbers themselves); I guess you mean an "integer".
For a triangle to exist the shorter two sides must be longer than the longest side. Thus there is an upper limit to the length of the longest side of a triangle.
For a given perimeter, the longest side must be less than half the perimeter. For a perimeter of 42cm this means that the longest side is less than 42 cm ÷ 2 = 21 cm.
If we focus on the longest side of a triangle, as it becomes shorter, one or both of the other two sides must increase in length, they can equal but never be longer than this longest side. Thus there is also a lower limit below which the longest side cannot be; this is when all three sides are equal and the triangle is an equilateral triangle. For a perimeter of 42cm the longest side is greater than or equal to 42 cm ÷ 3 = 14 cm
So with a perimeter of 42 cm we have:
14 cm ≤ longest side < 21 cm
Which means for an integer length, the longest side can be 14 cm, 15 cm, 16 cm, 17 cm, 18 cm, 19 cm or 20 cm.
Wiki User
∙ 7y ago
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