Answer:
w=20cm
Explanation:
Tough question.
We are not told whether the surface area is only what can be seem from the top, or does it include regions beneath the butterfly. I made the assumption it is from the top
I had to make an assumption that since the butterfies are similar, they wll have the same ratio of width and height. We will assume an "effective height," a value of height that when multiplied by the width will yield the correct surface area of 53 cm^2.
See the attached worksheet.
The effective height for the smaller butterfly is 13.25cm. This multiplied by the given width (4cm) produces the surface area of 53 cm^3. The ratio of width to height (w/h) is 0.302.
We've already made the assumption that the width to height of the larger butterfly will be the same. Now we can use the larger area (1325 cm^2) with the width to height ratio as follows:
Area = w*h
Since w/h is = 0.302, we can write w = 0.302h or h = (w/0.302)
1325 cm^2 = w*h
1325 cm^2 = w*(w/0.302)
w^2 = 200
w = 20 cm
(I made several assumptions in this analysis. Review them carefully).