two sides of a triangle measure 12 and 10. which inequality shows all the possible lengths of the third…
two sides of a triangle measure 12 and 10. which inequality shows all the possible lengths of the third side, x? a 2 < x < 22 b 10 < x < 12 c 0 < x < 22 d 3 < x < 21
Answer
Explanation:
Step1: Recall triangle - side rule
The length of the third side (x) of a triangle with side lengths (a) and (b) must satisfy the following two inequalities: (|a - b|\lt x) and (x\lt a + b).
Step2: Calculate the lower - bound
Given (a = 12) and (b = 10), the lower - bound is (|12 - 10|=2), so (2\lt x).
Step3: Calculate the upper - bound
The upper - bound is (12 + 10 = 22), so (x\lt22).
Answer:
A. (2\lt x\lt22)