GMAT Math : Calculating the perimeter of an acute / obtuse triangle
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Example Questions
Example Question #1 : Acute / Obtuse Triangles
A triangle has 2 sides length 5 and 12. Which of the following could be the perimeter of the triangle?
I. 20
II. 25
III. 30
All 3 are possible.
I and II only
I only
II and III only.
III only
II and III only.
For a triangle, the sum of the two shortest sides must be greater than that of the longest. We are given two sides as 5 and 12. Our third side must be greater than 7, since if it were smaller than that we would have 
Thus our perimeter will be between 
Example Question #2 : Acute / Obtuse Triangles
Triangle 
To calculate the perimeter, we simply need to add the three sides of the triangle.
Therefore, the perimeter is 
Example Question #3 : Acute / Obtuse Triangles
Triangle 
Since BD is the height of triangle ABC, we can apply the Pythagorean Theorem to, let's say, triangle DBC and 
Since the basis of the height is at the midpoint of AC, it follows that triangle ABC, is an isoceles triangle.
We can find the perimeter by multiplying BC by 2 and add the basis of the triangle AC, which has length of 
The final answer is therefore 
Example Question #4 : Acute / Obtuse Triangles
An acute triangle has side lengths of 
For any given triangle, the perimeter 
Example Question #5 : Acute / Obtuse Triangles
An acute triangle has side lengths of 
For any given triangle, the perimeter 
Example Question #6 : Acute / Obtuse Triangles
An acute triangle has side lengths of 
For any given triangle, the perimeter 
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