Question

If triangle ABC ~triangle PQR ar (triangle ABC )= 16 cm and ar( triangle PQR ) =81 .AB= 2cm find pq

Answer 1

(Side Ratio)^2 = Area ratio

Since these are similar triangles....


Thus, (AB/PQ)^2 = ar(ABC)/ar(PQR)

SO, AB/PQ = 4/9

OR, PQ = 9/2 = 4.5 cm

Answer 2

Since the triangles are similar

Therefore

Using the area of similar triangles
$\frac{(ar)tri \: \: abc }{(ar)tri \: \: pqr} = {( \frac{ab}{pq} )}^{2}$
$\frac{16}{81} = {(\frac{2}{pq}) }^{2}$
pq= 4.5 cm