In this question we are asked to calculate the other sides of a triangle using similarity when shortest side is 6 cm and which is similar to a triangle whose sides are 4 cm,7 cm and 8 cm.
ML Aggarwal Avichal Publication, Similarity, Chapter 13, Question no 7
Let us assume that, △ABC∼△DEF
△ABC is BC=6cm
△ABC∼△DEF
So, AB/DE=BC/EF=AC/DF
Consider AB/DE=BC/EF
AB/8=6/4
AB=(6×8)/4
AB=48/4
AB=12
Now, consider BC/EF=AC/DF
6/4=AC/7
AC=(6×7)/4
AC=42/4
AC=21/2
AC=10.5cm.