Question

Geometry

Two sides of a triangle have lengths 11 and 18. Write an inequality to represend the possible lengths for the third side, x.

Answer 1

Answer: 7 < x < 29

------------------------------------------------

Step-by-step explanation:

Let
a = 11
b = 18
c = x
be the three sides of the triangle

It turns out that if you know the two sides (a=11 and b=18) then you can figure out the range for the third side (c=x) using this inequality

b-a < x < b+a
Notice how 'b' is the larger value

So we can say,
b-a < x < b+a
18-11 < x < 18+11
7 < x < 29

Therefore x can be between 7 and 29 excluding both endpoints
The value of x cannot be 7 or a triangle won't form (instead a straight line will)
The value of x cannot be 29 or a triangle won't form (instead a straight line will)