Possible Side Lengths of Triangle
<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-possible-side-lengths-of-triangle" target="_blank">Possible Side Lengths of Triangle</a></span></p><p>Imagine we have the triangle below. This is just a generic triangle. Pretend we only know the two side lengths. None of the angles. We don't even know what it looks like.</p>
<p>What are the <strong><span style="color:#8e44ad;">Possible Side Lengths</span></strong> of $y$?</p>
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<p>Well, there are an infinite number of possibilities. Fortunately, they can be represented by an inequality produced by this formula.</p>
<p>$$(9-5) < y <(9+5)$$</p>
<p>$$4 < y <14$$</p>
<p>Side length $y$ must be larger than $4$ and smaller than $14$. If we consider <u><strong>only integer values</strong></u> for $y$, it must be either $5$, $6$, $7$, $8$, $9$, $10$, $11$, $12$, or $13$.</p>
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<p>For any generic triangle, the unknown side must be larger than the difference of the other two sides and smaller than their sum.</p>