Two sides of a triangle have lengths 9 and 15. What must be true about the length of the third side?

less than 9
less than 24
less than 6
less than 15

Question

Two sides of a triangle have lengths 9 and 15. What must be true about the length of the third side?
 	
	less than 9
	less than 24
	less than 6
	less than 15

yonce · Answer

HELP?

yonce · Answer

@jim_thompson5910

jim_thompson5910 · Answer

let a,b,c be the sides of the triangle

a = 9
b = 15
c = unknown

jim_thompson5910 · Answer

c can be any number you want as long as c is between 15-9 = 6 and 15+9 = 24

c cannot be equal to 6 or 24

so $\Large 6 < c < 24$

jim_thompson5910 · Answer

something like c = 20 will work but c = 100 is too big and c = 2 is too small

yonce · Answer

So less than 15?

jim_thompson5910 · Answer

no I have c < 24 so less than 24

jim_thompson5910 · Answer

at the same time, c is also larger than 6

jim_thompson5910 · Answer

c > 6 AND c < 24 means $\Large 6 < c < 24$

yonce · Answer

Oh I understand now. ok Thanks!

jim_thompson5910 · Answer

no problem