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# the sum of lengths of 2 sides of triangle must be greater than 3rd side. ?

If one side is 16 in and the second side is 2 in less than twice the third side ,what are the possible lengths for the second and third side?

### 3 Answers

- 1 decade agoFavorite Answer
*You cannot use the pythagoren theorem uness it is a right triangle and wedo not know if it is* (the pythagorean thm is a^2+b^2=c^2)

first thing i would do is draw a picture.

label one side 16in, another x and the third 2x-2 because the largest side will be the 2x-2 set up the equation 16+x=2x-2 solve the equation for x nd you get x=18 input this number into 2x-2 and you get 34

to check the answer see if the two small sides add up to the big one (they do) therefore you have a16, 18, 34 triangle

Hope this helps =)

- 1 decade ago
triangle, side 3 is the hypotanous. Side 2 is (c-2)so

c^2 = a^2 + b^2

c^2 = (c-2)^2 + 16^2

c^2 = c^2 - 4c +4+256

4c = 260

c=65

a=63

b=16

a+b>c

- 1 decade ago
sum of two shortest sides > longest side

S1+S3>S2

16+S3>2*S3-2

18+S3>2*S3

18>S3

S1=16

S2<34 and S2=(2*S3)-2

S3<18

Source(s): HighSchool math. It's been a few years but I think that's right.