Two sides of a triangle have lengths of 16 and 18. The length of the third side cannot be....30, 17, 7, or 1

Question

anonymous · Answer

please help, math is my week spot and now need help on this question a lot!

sparrow2 · Answer

it's 1 because the third side's length must be more than 18-16=2

sparrow2 · Answer

so if i have triangle and sides are a,b,c than for everyone(let's for b) is following:  a+c>b>a-c (a>c otherwise we consider c-a,it's same)

owlcoffee · Answer

This will be a little complex to explain, but I'll do my best.

We gave two given sides of a triangle and we want to find a possible third length.
Then we will take one of the sides, let's call them "a" wich is 16 and "b" wich is 18.
We will make one of them to be static, meaning that it is fixed in one position:
|dw:1432495207058:dw|

owlcoffee · Answer

Now, we will make a circle, wose radius is "b" meaning, the length of "b" on one of the extreme points of "a":
|dw:1432495447706:dw|
What the circumference does represent is all the points we can create a triangle with.
But you can see that there is a space between "a" and the circle, well, that little space defines the minimum length the third side can take, and if you draw it witch scale, you will see that it's 2 units of measure.
So therefore, the third side has to be minimum 2 units long.

kash_thesmartguy · Answer

It can't be 1 because the length of any two sides of triangles should be greater than the third one. So: 16+18 should be greater than 1 and it is greater than 1. 18+1 should be greater than 16 and it is greater than 16. 16+1 should be greater than 18 but it's not. So, 1 can't be the side of the triangle