Using the Triangle Inequality Theorem, form a system of three inequalities and solve it.
From 132 to 618 miles.
Practice makes perfect
It is given that the distance between San Jose and Las Vegas is about 375 miles, and between Las Vegas and Carlsbad is about 243 miles. Let's plot a triangle to illustrate this situation.
Now, let's recall what the Triangle Inequality Theorem states.
The sum of the lengths of any two
sides of a triangle must be greater
than the length of the third side.
Let the distance between San Jose and Carlsbad be x miles. Using this theorem, we can write the following three inequalities.
375+243>x
375+x>243
x+243>375
Let's solve these inequalities for x.
Inequality
Solution Set
375+243>x
618>x
375+x>243
x>- 132
x+243> 375
x>132
Now we can solve the system of these three inequalities by graphing.
All three lines overlap on the segment from 132 to 618. Therefore, the possible distance from San Jose to Carlsbad is between 132 to 618 miles.
