Since `DE||BC`, we have
`angle ADE= angle ABC` (corresponding `angle`]
and `angle AED= angle ACB` ( corresponding `angle`)
`:. Delta ADE~ Delta ABC` [ by AA- similarity] So, the corresponding sides of `Delta ADE and Delta ABC` are proportinal.
`:. (AD)/(AB)=(DE)/(BC)=(AE)/(AC)" "....(i)`
Now, `(AD)/(AB)=(DE)/(BC) rArr (2)/(4.5)=(4)/(BC) [ :. AB=AD+BD=4.5 cm]`
`rArr BC=((4xx4.5)/(2)) cm=9 cm`.
Again, `(DE)/(BC)=(AE)/(AC)` [ from (i)]
`rArr (4)/(9)=(3.2)/(AC) [ :. BC=9 cm]`
`rArr AC=((9xx3.2)/(4)) cm ==7.2 cm`
Hence, `AC=7.2 cm and BC= 9=cm`
