Answer:
Yes, the triangles are similar.
x=7.2
Step-by-step explanation:
Similar triangles are triangles which have the same shape not not the same size. This can be seen when triangles have the same exact angle measures. The triangles in number 4 have the exact same angle measures and are therefore similar. Because they are similar, their sides have a special relationship. They are proportional on each triangle. We can set a proportion to find an unknown length.
A proportion is a ratio between two related quantities. We will write a proportion from one triangle side to the corresponding side on the other.
[tex]\frac{3}{5} =\frac{x}{12} \\[/tex]
We can cross multiply and isolate x to solve.
[tex]\frac{3}{5} =\frac{x}{12}\\3(12)=5(x)\\36=5x\\\frac{36}{5} =\frac{5x}{5} \\7.2=x[/tex]
