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Example Question #232 : Plane Geometry
If a = 7 and b = 4, which of the following could be the perimeter of the triangle?
I and II Only
II and III Only
I, II and III
Consider the perimeter of a triangle:
P = a + b + c
Since we know a and b, we can find c.
11 = 7 + 4 + c
11 = 11 + c
c = 0
Note that if c = 0, the shape is no longer a trial. Thus, we can eliminate I.
15 = 7 + 4 + c
15 = 11 + c
c = 4.
This is plausible given that the other sides are 7 and 4.
25 = 7 + 4 + c
25 = 11 + c
c = 14.
It is not possible for one side of a triangle to be greater than the sum of both of the other sides, so eliminate III.
Thus we are left with only II.
Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle
Which of the following measurements can NOT represent the sides of a triangle.
Given the Triangle Inequality, the sum of any two sides of a triangle must be greater than the third side.
Given the measurements :
Therefore, these lengths cannot represent a triangle.