Question

Question #a64db

Answer 1

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)`