Calculating the perimeter of an acute / obtuse triangle - GMAT Quantitative Reasoning
Card 0 of 6
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
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
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 
where 
is the unknown side. It must also be smaller than 17 since were it larger, we would have 
.
Thus our perimeter will be between 
and 
. Only II and III are in this range.
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
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Triangle 
has sides 
. What is the perimeter of triangle 
?
Triangle
To calculate the perimeter, we simply need to add the three sides of the triangle.
Therefore, the perimeter is 
, which is the final answer.
To calculate the perimeter, we simply need to add the three sides of the triangle.
Therefore, the perimeter is
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Triangle 
has height 
. If 
is the midpoint of 
and 
, what is the perimeter of triangle 
?
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 
.
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
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An acute triangle has side lengths of 
, 
, and 
. What is the perimeter of the triangle?
An acute triangle has side lengths of
For any given triangle, the perimeter 
is the sum of the lengths of its sides. Given side lengths of 
, 
, and 
, 
.
For any given triangle, the perimeter
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An acute triangle has side lengths of 
, 
, and 
. What is the perimeter of the triangle?
An acute triangle has side lengths of
For any given triangle, the perimeter 
is the sum of the lengths of its sides. Given side lengths of 
, 
, and 
, 
.
For any given triangle, the perimeter
Compare your answer with the correct one above
An acute triangle has side lengths of 
, 
, and 
. What is the perimeter of the triangle?
An acute triangle has side lengths of
For any given triangle, the perimeter 
is the sum of the lengths of its sides. Given side lengths of 
, 
, and 
, 
.
For any given triangle, the perimeter
Compare your answer with the correct one above