When two triangles are similar, they're sides are in proportion.
In order to find the unknown side, we first have to find the ratio of the larger triangle to the smaller triangle.
We can use the sides TV and LN to make the proportion.
[tex]\frac{LN}{TV}[/tex] = [tex]\frac{21}{6}[/tex]
The ratio between the two triangles is 21:6
Now we can solve for the unknown side.
[tex]\frac{21}{6}[/tex] = [tex]\frac{LM}{8}[/tex]
Cross multiply:
8 * 21 = 6 * LM
168 = 6LM
Divide both sides by 6:
LM = 28
The unknown side's length is 28 centimeters
Good luck!
