Triangle Inequality Theorem is fair game on the SAT, ACT, GRE, or GMAT. It’s often forgotten by test-takers, but when it pops up, you’ll be glad you know it! The theorem essentially states that the third side of a triangle must be between the difference and sum of the other two sides.
For example, if we had a triangle in which two sides were 6 and 9, then the third side must be between 3 (9-6) and 15 (9+6). The third side cannot actually equal 3 or 15, it’s important to remember.
Let’s try a practice question utilizing this math rule!
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?
B) I only
C) II only
D) II and III only
E) I,II and III
If two of the sides are 2 and 5. Then the range of possible values for the third side can be expressed as:
3 < x < 7
Perimeter is the sum of the sides. Let’s choose 3 and 7 as values for the 3rd side (even though we know they are the end-limits only) to create a range for the perimeter.
On the low end:
2 + 5 + 3 = 10
On the upper end:
2 + 5 + 7 = 14
So the perimeter range can be expressed as:
10 < x < 14
The perimeter must be BETWEEN 10 and 14. The answer is (A).
Here’s a link to a lot of great Triangle review topics if you want more Geometry practice: http://www.beatthegmat.com/mba/category/tags/gmat-math/geometry/triangles.