Suppose the sides of #triangleA# are
#color(white)("XXX")P_A=48, Q_A=36, and R_A=54#
with corresponding sides of #triangleB#:
#color(white)("XXX")P_B, Q_B, and R_B#
#{:
("Given:",,,,,),
(,P_A,color(white)("xx"),Q_A,color(white)("xx"),R_A),
(,48,color(white)("xx"),36,color(white)("xx"),54),
("Possibilities:",,,,,),
(,P_B,color(white)("xx"),Q_B,color(white)("xx"),R_B),
(,5,color(white)("xx"),5/48 * 36=3 3/4,color(white)("xx"),5/48*54=5 5/8),
("or",5/36 * 48=6 2/3,color(white)("xx"),5,color(white)("xx"),5/36*54=7 1/2),
("or",5/54*48=4 4/9,color(white)("xx"),5/54*36=3 1/3,color(white)("xx"),5)
:}#