Answer:
Side LM has a length of 28 centimeters.
Step-by-step explanation:
Similar triangles are those that are related by a proportion, that is, they have a scale ratio in common.
You can notice in the image that the given triangles are similar, that means we can deduct the proportion
[tex]\frac{TV}{LN}=\frac{TU}{LM}[/tex]
Replacing each value, we have
[tex]\frac{6}{21}=\frac{8}{x}[/tex]
Then, we solve for [tex]x[/tex]
[tex]6x=168\\x=\frac{168}{6}\\ x=28[/tex]
And, [tex]LM=x=28[/tex]
Thereofore, side LM has a length of 28 centimeters.
