Given that,
AB=2x+1
BC=x+1,
let,
AC=x
Area of triangle=1/2?base?height
? ?60=1/2?(2x+1)?(x+1)
? ? 120=(2x+1)(x+1)
? ? 120=2x?+2x+x+1
? ? 120=2x?+3x+1
? ?2x?+3x-119=0
? 2x?+17x-14x-119=0
?x(2x+17) -14(x+17)=0
(2x+17)(x-14)=0
x=14 is answer
AB=29cm
BC=15cm