Triangles

[naveenhv]

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

a. None
b. I only
c. II only
d. II and III only
e. I,II and III

[VivianKerr]

Hi Naveen,

This question is testing Triangle Inequality Theorem, which states that for any triangle the length of the third side must be BETWEEN the sum and the difference of the other two sides.

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: https://www.beatthegmat.com/mba/category ... /triangles