At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine the range of possible values for the third side [tex]\( x \)[/tex] in a triangle with sides measuring 200 units and 300 units, we use the triangle inequality theorem. According to this theorem, in any triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
To find this range for the third side [tex]\( x \)[/tex], follow these steps:
1. Calculate the Difference of the Given Sides:
[tex]\[ \text{Difference} = |200 - 300| = 100 \][/tex]
2. Calculate the Sum of the Given Sides:
[tex]\[ \text{Sum} = 200 + 300 = 500 \][/tex]
3. Set Up the Compound Inequality:
The length of the third side [tex]\( x \)[/tex] must be greater than the difference and less than the sum of the other two sides:
[tex]\[ 100 < x < 500 \][/tex]
Thus, the compound inequality that represents the range of possible lengths for the third side [tex]\( x \)[/tex] is:
[tex]\[ 100 < x < 500 \][/tex]
This means the length of the third side must be more than 100 units and less than 500 units.
To find this range for the third side [tex]\( x \)[/tex], follow these steps:
1. Calculate the Difference of the Given Sides:
[tex]\[ \text{Difference} = |200 - 300| = 100 \][/tex]
2. Calculate the Sum of the Given Sides:
[tex]\[ \text{Sum} = 200 + 300 = 500 \][/tex]
3. Set Up the Compound Inequality:
The length of the third side [tex]\( x \)[/tex] must be greater than the difference and less than the sum of the other two sides:
[tex]\[ 100 < x < 500 \][/tex]
Thus, the compound inequality that represents the range of possible lengths for the third side [tex]\( x \)[/tex] is:
[tex]\[ 100 < x < 500 \][/tex]
This means the length of the third side must be more than 100 units and less than 500 units.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.