Two side lengths of a triangle are 11 and 17. What is the longest possible integer length of the third side of the triangle?

Dont know where to start

jeffthememeguy Jan 21, 2021

#1**+3 **

use the good ol' pythagorean theorem

a^2+b^2=c^2

11^2+17^2=410

x^2=410

**sqrt410** (can't be simplified any further)

KitSoundwave Jan 21, 2021

#3**-1 **

I tried this when I did it, and it wasn't right, but Cphill gave a simple answer which used triangle inequality. Great answer though, I can see why you got that

jeffthememeguy
Jan 21, 2021

#2**+2 **

Got to be careful here.....we might not necessarily have a right triangle

In general.....The sum of any two sides of a triangle is greater than the remaining side (this is known as the trinagle inequality)

So

11+ 17 = 28

So the remaining side must be < 28 = 27

CPhill Jan 21, 2021

#4**-1 **

Thanks so much! I'll definitely do a little bit more research on triangle inequality

jeffthememeguy
Jan 21, 2021