Calculate the other sides of a triangle whose shortest side is 6cm and which is similar to a triangle whose sides are 4cm, 7cm and 8cm.

Let △ABC ~ △DEF in which shortest side of △ABC be BC = 6cm.
△DEF, DE = 8cm, EF = 4cm and DF = 7cm.

Since, △ABC ~ △DEF so,

$\dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{AC}{DF} \\[1em] \text{Consider, } \dfrac{AB}{DE} = \dfrac{BC}{EF} \\[1em] \dfrac{AB}{8} = \dfrac{6}{4} \\[1em] AB = \dfrac{48}{4} \\[1em] AB = 12.$

Now consider,

$\dfrac{BC}{EF} = \dfrac{AC}{DF} \\[1em] \dfrac{6}{4} = \dfrac{AC}{7} \\[1em] AC = \dfrac{42}{4} \\[1em] AC = 10.5.$

Hence, the other sides of triangle are 10.5cm and 12cm.