Start with determining the range of possible lengths of the third side by using the Triangle Inequality Theorem.
1/2
Practice makes perfect
A student has 6 cm long and 9 cm long two straws. Let's use the Triangle Inequality Theorem to help her to find the range of possible lengths of the third side which allows her to form a triangle.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The illustration of the theorem is given below.
XY+YZ>XZ
YZ+XZ>XY
XZ+XY>YZ
Let x cm be the length of the third side. Applying the theorem, we have three inequalities.
Inequality I:&6+9>x ⇒ 15 > x
Inequality II:&9+x>6 ⇒ x > -3
Inequality III:&x+6>9 ⇒ x > 3
According to the inequalities, the range for the possible lengths of the third side can be obtained by combining Inequality I and III as follows.
3 cm< x< 15 cm
As a result, if she picks 5 cm and 11 cm long straws from the group of four straws, she can form a triangle. In this case, we can find the probability as follow.
