GMAT question - What is the area of a triangle... - Review
Type: Problem Solving
Difficulty: 
- 30
- 32.5
- 60
- 65
- 130
Explanation
Firstly we should draw a picture of the triangle described. We are told that it is
a triangle with a perimeter of 36 and two sides of length 13
So we can draw
We know that the total perimeter is 36 so we can work out the length of the base.
So we know that the base of the triangle has length 10. Adding this information to our diagram gives us.
The area of a triangle equals . We already know the base is 10 so to find the area of this triangle we need to work out the height.
If we draw in the height of the triangle into the diagram you can see that it will splits the figure into two right-angled triangles with base 5 and hypotenuse 13.
We could use the Pythagoras theorem to find the height but those GMAT students who have prepared themselves will save precious minutes because they will recognize that a right-angled triangle with base length 5 and a hypotenuse length 13 is a 5-12-13 triangle, one of the triangles that commonly appears in the GMAT.
Therefore the height of the triangle is 12.
Now we can work out the area of this triangle which has a base of length 10 and a height of 12.
Therefore the correct answer is C.
It has B highlighted when C is the correct answer.
Oops. Thank you very much for pointing out this mistake, it has been fixed now.
It would be more clear if the question states that.....if the length of two sides is 13 units each
Good point. I've modified the question to make this clearer.