Question

i dont understand these types of problems can someone help: The lengths of 2 sides of the triangle are given. The length of the third side must be greater than ____ but less than __.
some examples:
6,9
15,13
7n,10n

Answer 1

@jim_thompson5910

Answer 2

if the sides of the triangle are a,b,c


and if you know the sides of a,b, then the third side c is subject to the following


a-b < c < a+b

Answer 3

in this case, a > b

Answer 4

yeah i get that part

Answer 5

for example, say we have a triangle with sides of 10, 12, x

in this case, a = 12, b = 10, c = x

so...

a-b < c < a+b

12-10 < x < 12+10

2 < x < 22

so the third side is between 2 and 22 (not including 2 and not including 22)

Answer 6

yeah i get that you add them and subtract them but for one the numbers are 15 and 20 and the answer key says 3 and 15

Answer 7

well if the two given sides are known to be 15 and 20, then the third side c is between 20-15 = 5 and 20+15 = 35

so

5 < c < 35

Answer 8

I have no idea how they got 3 and 15. Three is too small. Also, you can go higher than 15.

Answer 9

oh i was reading the wrong one it was for 6 and 9

Answer 10

so 9-6 = 3 and 9+6 = 15

which I'm sure you see by now

Answer 11

yeah i got it now thanks so much for the help!!

Answer 12

you're welcome