Question
Find the range of possible measures of
the third side. Use the variable
.
the third side. Use the variable
Ask by Powers Hardy. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The third side
must be greater than 3 and less than 11.
Solution

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The Deep Dive
To find the range of possible measures for the third side
of a triangle with sides 4 and 7, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
-
For the sides 4 and
: -
For the sides 7 and
: (but since must be positive, this isn’t a restriction) -
For the sides 4 and 7:
Combining these results, the range of
is:
So, the possible measures for the third side
fall between 3 and 11.