Question

Medals?

Answer 1

4. A pair of corresponding sides of two similar pentagons have lengths of 12 cm and 28 cm. What is the ratio of the areas of the two pentagons?
A. 12/28
B. 27/343
C. 28/12
D. 9/49

Answer 2

There are a few different formulas for finding the area of a pentagon. The one I recommend for this problem is

A=(sqrt(5(5+2*sqrt(5)))*a^2)/4

This is a big formula, but you could use it to find the areas. However, in this case we only want the ratio of the areas. That means that we will set up a fraction, plugging 12 into that equation for the numerator, and 28 into the bottom for the demoninator. The nice thing about doing it as a fraction means that all the constants will cancel out. that will leave just 12^2/28^2 as our ration. Simplifying this gives us:

12^2/28^2 = (12/28)^2 = (3/7)^2 = 9/49

Which is answer D of your choices