We have been given the following side lengths.
19.5 ft 20.5 ft
We can find the range of possible lengths for the third side of the triangle, x ft, 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:&19.5+20.5>x ⇒ 40 > x
II:&20.5+x>19.5 ⇒ x > -1
III:&x+19.5>20.5 ⇒ x > 1
The range for the possible lengths of the third side can be found by looking at the overlapping regions for these inequalities.
