Name the length of two legs with some variable. Then form a system of three inequalities for the measures of the triangle's sides using the Triangle Inequality Theorem.
Greater than 3
Practice makes perfect
We are told that the base of the isosceles triangle measures 6 inches. Let the measure of its two sides of equal length be x inches.
Now, to find the possible values of x we will use the Triangle Inequality Theorem, which states the following.
The sum of the lengths of any two
sides of a triangle must be greater
than the length of the third side.
Using this theorem, we can form three inequalities for our isosceles triangle.
x+x>6
x+6>x
6+x>x
Note that since its an isosceles triangle the last inequalities are the same. Thus, we need to solve the system of the two first inequalities.
x+x>6
x+6>x
2x>6
6>0
x>3
All solutions.
As we can see, the second inequality simplifies to 6>0, which is always true. This means that only the first inequality estimates x. Therefore, the length of each leg of the isosceles triangle must be greater than 3.
