If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
1. x ≤ 5 ≤ 8 then x + 5 > 8 → x > 8 - 5 → x > 3 therefore 3 < x ≤ 5.
2. 5 ≤ x ≤ 8 then 5 + x > 8 → x > 3 therefore 5 ≤ x ≤ 8
3. 5 ≤ 8 ≤ x then 5 + 8 > x → 13 > x → x < 13 therefore 8 ≤ x < 13.
Answer:
3 < x < 13
Step-by-step explanation:
Since, a triangle is possible when the sum of any two sides is greater than the third side,
Given,
The sides of the triangle are 5 inches and 8 inches,
If x shows the third side,
Then, by the above statement,
x < 5 + 8 ⇒ x < 13
5 < x + 8 ⇒ -3 < x
8 < x + 5 ⇒ 3 < x
Hence, the required inequality gives the range of possible values for x is,
3 < x < 13
