Dentonboys03idn
Answered

Discover the best answers to your questions with the help of IDNLearn.com. Get prompt and accurate answers to your questions from our experts who are always ready to help.

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, [tex]x[/tex].

Sagot :

GinnyAnsweridn
To determine the possible length of the third side, [tex]\( x \)[/tex], in a triangle with side lengths of 200 units and 300 units, we use the triangle inequality theorem. This theorem states that the length of any side of a triangle must be greater than the absolute value of the difference of the other two sides and less than the sum of the other two sides.

First, let's find the lower bound for [tex]\( x \)[/tex]:

[tex]\[ x > |200 - 300| \][/tex]
[tex]\[ x > 100 \][/tex]

Next, let's find the upper bound for [tex]\( x \)[/tex]:

[tex]\[ x < 200 + 300 \][/tex]
[tex]\[ x < 500 \][/tex]

Combining these inequalities, we get the compound inequality that describes the possible lengths for the third side [tex]\( x \)[/tex]:

[tex]\[ 100 < x < 500 \][/tex]

So, the range of possible lengths for the third side is:

[tex]\[ 100 < x < 500 \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.