9514 1404 393
Answer:
6 < x < 14
Step-by-step explanation:
The shortest the third side can be is the difference between the given sides:
10 -4 = 6
The longest the third side can be is the sum of the given sides:
10 +4 = 14
So the inequality for side length x is ...
6 < x < 14
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More detail
These come from the triangle inequality, which requires ...
a + b > c; b + c > a; c + a > b
Filling in 4, 10, and x, these become ...
- 4 + 10 > x ⇒ 14 > x . . . from the sum of the two given sides
- 10 + x > 4 ⇒ x > -6 . . . . . less restrictive than the next
- x + 4 > 10 ⇒ x > 6 . . . from the difference of the two given sides
In summary, 6 < x < 14.
