A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?

Question

A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?

1.  Yes, because 4 + 5 > 8 
2. Yes, because 5 + 8 < 4 
3. No, because 4 + 5 > 8 
4. No, because 5 + 8 > 4

Answer 1

Given 3 positive real numbers as the lengths of a possible triangle, a triangle is possible only if the sum of any two sides is greater then the length of the 3rd side.

Given: 4, 5, and 8.then

4 + 8 > 5

5 + 8 > 4

And finally:

4 + 5 > 8.

Focus on the two short sides. That sum must be greater than the largest of the 3 numbers.

Say you were given: 3, 4, 7.

3 + 4 is not greater then 7. Picture the side of length 7 if you lay the 3 and the 4 along that side those segments would overlay the 7 (no triangle).

Answer 2

Hi Egeg,

The correct answer is:

Yes, because 4 + 5 > 8

In order for a triangle to be formed with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, 4+5 > 8, 4+8 > 5, 5+8 > 4, so a triangle can indeed be formed with side lengths 4 in, 5 in, and 8 in.