# Triangle A has sides of lengths 36 , 42 , and 40 . Triangle B is similar to triangle A and has a side of length 3 . What are the possible lengths of the other two sides of triangle B?

$\textcolor{w h i t e}{\text{XXX}} \left(\frac{7}{2} , \frac{10}{3}\right) \mathmr{and} \left(\frac{18}{7} , \frac{20}{7}\right) \mathmr{and} \left(\frac{27}{10} , \frac{63}{20}\right)$
{: (,,"|",A_1=36,"|",A_2=42,"|",A_3=40), ("if " B_1=3,,"|",,"|",,"|",), (,rarrB_i/A_i=1/12,"|",,"|",,"|",), (,,"|",,"|",B_2=42/12=7/2,"|",B_3=40/12=10/3), ("if " B_2=3,,"|",,"|",,"|",), (,rarrB_i/A_i=1/14,"|",,"|",,"|",), (,,"|",B_1=26/14=18/7,"|",,"|",B_3=40/14=20/7), ("if " B_3=3,,"|",,"|",,"|",), (,rarrB_i/A_i=3/40,"|",,"|",,"|",), (,,"|",B_1=(36xx3)/40=27/10,"|",B_2=(42*3)/40=63/20,"|",) :}