Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

If the ratio of the corresponding side lengths of two similar polygons is 5:9, what is the ratio of their areas?

A. 5:9
B. 10:9
C. 25:81
D. 10:81

Please select the best answer from the choices provided:
A.
B.
C.
D.

Sagot :

GinnyAnswer
Sure, let's break this down step-by-step.

When dealing with similar polygons, the areas of these polygons are related to the square of the ratios of their corresponding side lengths. This is important and can be derived from the properties of similar polygons.

1. Determine the side length ratio: The given ratio of the corresponding side lengths is 5:9.

2. Square the side length ratio: To find the ratio of their areas, we need to square the lengths of the sides. This is because the areas of similar polygons are proportional to the squares of their corresponding side lengths.

- The square of the ratio 5:9 is calculated as follows:
- [tex]\(5^2\)[/tex]:[tex]\(9^2\)[/tex]
- [tex]\(25\)[/tex]:[tex]\(81\)[/tex]

3. Conclusion: Based on the squared ratio of the side lengths, the ratio of the areas of the two similar polygons is 25:81.

So, the best answer from the choices provided is:
C. 25:81
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.