Question #a64db

1 Answer
Nov 22, 2016

See below.

Explanation:

Supposing the area of DeltaABC is given by (b_1 h_1)/2 and the area of DeltaPQR is given by (b_2h_2)/2 If they are similar by lambda = a/b the their areas are similar by lambda^2 because

(a_2b_2)/2=((lambda a_1)(lambda b_1))/2=lambda^2(a_1,b_1)/2 so finally

(((a_2b_2)/2)/((a_1b_1)/2))=lambda^2=(a^2/b^2)