Question

Triangles QVS and RTS are similar. Find side VS.

Answer 1

Given that "Triangles QVS and RTS are similar".

We know that ratio of corresponding sides in similar triangles are equal so we will use that property here.

Possible ratio of corresponding sides are:

QV/RT=VS/TS=QS/RS

Now plug the given values from the picture.

26/10=x/28=QS/RS

or 26/10=x/28

or 26*28=10*x (cross multiplication)

or 728=10*x

or 728/10= x

or 72.8=x

Hence final answer is side VS=x=72.8

Answer 2

If these triangles are similar then side QV is corresponding and proportionate to side RT; and side VS is corresponding and proportionate to side VS. We could set up a proportion as follows for these triangles with the larger triangle "stuff" on top and the smaller on bottom:

$\frac{26}{10}=\frac{x}{28}$.

We cross-multiply to get 10x = 728 and divide both sides by 10 to get that side VS = 72.8