Question

4. Can a triangle have sides with the given lengths?
7 cm, 13 cm, 6cm

Answer 1

No

Explanation:

The triangle inequality theorem tells us that the sum of any two sides of a triangle MUST BE GREATER than the third side.

Let's check the options. Remember, has to be GREATER, NOT GREATER THAN OR EQUAL TO.

7 + 13 = 20

is it greater than 6? YES

7 + 6 = 13

is it greater than 12? NO [equal]

13 + 6 = 19

is it greater than 7? YES

So, triangle inequality theorem doesn't hold. It has to hold for all 3 conditions. So, a triangle CANNOT HAVE these sides lengths.