# Given 2 similar triangles. Triagle1 has 2 sides known: 5cm

Given 2 similar triangles. Triagle1 has 2 sides known: 5cm and 3cm. The similar sides of the second triangle are equal to 45cm and 2x+13cm. Find the value of x.

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Mitchel Aguirre

Since the triangles are similar:
$$\displaystyle\frac{{5}}{{45}}=\frac{{3}}{{{2}{x}+{13}}}$$
Isolate x
$$\displaystyle{2}{x}+{13}=\frac{{{3}{\left({45}\right)}}}{{5}}$$
$$\displaystyle{2}{x}=\frac{{135}}{{5}}-{13}$$
$$\displaystyle{2}{x}={27}-{13}$$
$$\displaystyle{x}=\frac{{14}}{{2}}$$
$$x=7$$

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