Step-by-step explanation:
we don't need to actually do the detailed area calculation.
all we need to consider is that an area, ANY area (for triangles, rectangles,...) is always the product or the sum of products of 2 dimensions (like side lengths).
the scaling factor of similar objects (incl. triangles of course) applies to each individual line, length, height or side.
so, when calculating the area of a similar figure, the scaling factor has to be multiplied in twice (once for every multiplied dimension) - making it the square of the normal single-dimensional scaling factor.
so, in other words, the area scaling factor is the square of the side scaling factor.
coming from A1 to A2 the area scaling factor is
80/45 = 16/9
the side scaling factor is then
sqrt(16/9) = 4/3
we have to multiply a side of A1 by 4/3 to get the corresponding side of A2.
and so, the ratio of A1 side lengths to A2 side lengths is
3:4
(the inverse, upside-down form of the scaling factor as a consequence of the question "how do I convert the 3 length units of A1 into 4 length units of A2 ?" by multiplying the 3 units by the scaling factor 4/3).
