Answer:
2.8 < x < 5.8
Step-by-step explanation:
We must apply the Triangle Inequality Theorem which states that for any triangle with sides a, b, and c:
a + b > c
b + c > a
c + a > b
Here, let's arbitrarily denote a as 4.1, b as 1.3, and c as x. So, let's plug these values into the 3 inequalities listed above:
a + b > c ⇒ 4.1 + 1.3 > x ⇒ 5.8 > x
b + c > a ⇒ 1.3 + x > 4.1 ⇒ x > 2.8
c + a > b ⇒ x + 4.1 > 1.3 ⇒ x > -2.8
Look at the last two: clearly if x is greater than 2.8 (from the second one), then it will definitely be greater than -2.8 (from the third), so we can just disregard the last inequality.
Thus, the range of possible sizes for x are:
2.8 < x < 5.8
~ an aesthetics lover
