Question

A triangle has sides measuring 5 inches and 8 inches. If x represent the length in inches of the third side , which inequality gives the range of possible values for x ?

Answer 1

3 < x < 13

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

Answer 2

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 → S = (3, 13)