Δ PQR is similar to Δ DEF. If the ratio of their perimeters is 3 : 2, then the ratio of their areas is?
Answer & explanation
Correct answer: option 3
Δ PQR ∼ Δ DEF
⇒ \(\frac{Perimeter\;of\;Δ PQR}{Perimeter\;of\;Δ DEF}\) = \(\frac{PQ}{DE}\) = \(\frac{3}{2}\)
⇒ \(\frac{area\;of\;Δ PQR}{area\;of\;Δ DEF}\) = \(\frac{PQ^2}{DE^2}\) = \(\frac{3^2}{2^2}\) = \(\frac{9}{4}\)