Use the Triangle Inequality Theorem to form three inequalities and find their common solution by graphing.
From 20 to 200 feet
Practice makes perfect
We are given that the distance between the science classroom and lockers is 90 feet, and between the lockers and the math classroom is 110 feet. Let's illustrate this situation with a triangle.
Now let's review what the Triangle Inequality Theorem states.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
We can use this theorem to form three inequalities that are true for the triangle. In order to do this we can let the distance between the science classroom and the math classroom be x feet.
90+110>x
90+x>110
x+110>90
Let's solve these inequalities by isolating x on one side of each inequality.
Inequality
Solution Set
90+110>x
200>x
90+x>110
x>20
x+110>90
x>- 20
We can find the common solutions of these three solution sets by graphing them.
All three lines overlap on the segment from 20 to 200. Therefore, the possible distance between the science classroom and math classroom is between 20 to 200 feet.
