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olga2289 [7]
3 years ago
15

How do you find the missing side??

Mathematics
2 answers:
dexar [7]3 years ago
6 0
The answer is 12 if I’m not mistaken
guapka [62]3 years ago
4 0

Answer:

\boxed{\ell = 12}.

Step-by-step explanation:

Let \ell denote the length of the missing side. Since \triangle ABC and \triangle AXY share one vertex and \overline{XY}\parallel \overline{BC}, these triangles are similar. This means that:

\dfrac{AX}{AB} = \dfrac{AY}{AC} \iff \dfrac{\ell}{18+\ell} = \dfrac{14}{14+21} \iff\dfrac{\ell}{18+\ell} = \dfrac{14}{35}.

We now multiply both sides by 18+\ell and solve the equation:

\dfrac{\ell}{18+\ell} = \dfrac{14}{35} \iff \ell = \dfrac{36}{5} + \dfrac{14}{35}\ell \iff \ell \left(1-\dfrac{14}{35}\right) = \dfrac{36}{5} \iff \dfrac{3}{5}\ell = \dfrac{36}{5}.

So we now simply get:

\boxed{\ell = \dfrac{36}{3} = 12}.

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