Question

The ratio of the areas of two similar polygons is 49:16. If the perimeter of the first polygon is 22 cm, what is the perimeter of the second polygon?

Answer 1

1st: either 22 [ 7/4] or 22 [4/7]...if 22 is for smaller or for the larger...to see this consider the similar triangles ...let the smaller have base 2a and height b { area = ab } then the larger is of the form base 2aK and height bK { area ab K² }..ratio of areas is K² = 49/16 --> K = 7 / 4

3rd: as written the side length is [1/2] of the original side length...what is difficult about that ?

Answer 2

Answer:

The Area of the second polygon is 7.18 $cm^{2}$

Step-by-step explanation:

Great question, ratio problems are always fun because we can use a simple property called the Rule of Three to solve them in a really easy way. As shown on the picture below.

Assuming that the first polygon is the Larger Polygon we can write the following,

22 ⇒ 49

 x  ⇒ 16

$x = \frac{22*16}{49}$

$x = \frac{352}{49}$

$x = 7.18$

So we can see that the Area of the second polygon is 7.18 $cm^{2}$

** IF the First Polygon is actually the smaller one just replace the 49 and 16 in the formula and solve the same way**

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