Question

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?

Answer 1

The other two sides of B are
`color(white)("XXX")(7/2,10/3) or (18/7,20/7) or (27/10,63/20)`

Explanation:

#{: (,,"|",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,"|",) :}#