enter the correct answer in the box. a triangle has side lengths of 200 units and 300 units. write a…
enter the correct answer in the box. a triangle has side lengths of 200 units and 300 units. write a compound inequality for the range of the possible lengths for the third side, x.
Answer
Explanation:
Step1: Recall triangle - inequality theorem
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. Let the two given side - lengths be (a = 200) and (b = 300).
Step2: Calculate the lower - bound
The difference between the two given sides gives the lower - bound of the third side. So, (|a - b|\lt x), which is (|200 - 300|=100\lt x).
Step3: Calculate the upper - bound
The sum of the two given sides gives the upper - bound of the third side. So, (x\lt a + b), which is (x\lt200 + 300=500).
Answer:
(100\lt x\lt500)