Find the range of possible measures of
the third side. Use the variable .

Question

Find the range of possible measures of the third side. Use the variable $$ x $$. $$ 4,7 $$

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To find the range of possible measures for the third side $$ x $$ of a triangle when the other two sides are given as $$ 4 $$ and $$ 7 $$, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given the sides $$ a = 4 $$ and $$ b = 7 $$, we can set up the following inequalities based on the triangle inequality: 1. $$ a + b > x $$ 2. $$ a + x > b $$ 3. $$ b + x > a $$ Now, let's substitute the values of $$ a $$ and $$ b $$ into these inequalities: 1. $$ 4 + 7 > x $$ 2. $$ 4 + x > 7 $$ 3. $$ 7 + x > 4 $$ Now, we will simplify each inequality: 1. $$ 11 > x $$ or $$ x < 11 $$ 2. $$ x > 3 $$ 3. $$ x > -3 $$ (This inequality is always true since $$ x $$ must be positive) From the first two inequalities, we can combine them to find the range of $$ x $$: - From $$ x < 11 $$ - From $$ x > 3 $$ Thus, the range of possible measures for the third side $$ x $$ is: $$ 3 < x < 11 $$ This means that $$ x $$ can take any value greater than $$ 3 $$ and less than $$ 11 $$. The third side $$ x $$ must be greater than 3 and less than 11.

Find the range of possible measures of
the third side. Use the variable .

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Find the range of possible measures of the third side. Use the variable .

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Find the range of possible measures of
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