We have been given the following side lengths.
16 in. 26 in.
We can find the range of possible lengths for the third side of the triangle, x in., using the Triangle Inequality Theorem. This theorem tells us that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
XY+YZ>XZ
YZ+XZ>XY
XZ+XY>YZ
Applying this theorem to the given side lengths, we have three inequalities.
I:&16+26>x ⇒ 42 > x
II:&26+x>16 ⇒ x > -10
III:&x+16>26 ⇒ x > 10
The range for the possible lengths of the third side can be found by looking at the overlapping regions for these inequalities.
