Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Ask your questions and receive precise answers from experienced professionals across different disciplines. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Select the correct answer.
Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which statement is true?
O A.
The area of pentagon ABCDE is 216 times the area of pentagon PQRST
B.
C.
O D.
The area of pentagon ABCDE is 12 times the area of pentagon PQRST.
The area of pentagon ABCDE is 36 times the area of pentagon PQRST
The area of pentagon ABCDE is 6 times the area of pentagon PQRST.

Sagot :

GinnyAnswer
To solve this problem, we need to understand how the areas of similar figures are related given a scale factor.

Let the side length of pentagon PQRST be [tex]\( s \)[/tex]. Therefore, the side length of pentagon ABCDE is [tex]\( 6s \)[/tex] (since it's given that ABCDE is 6 times the side length of PQRST).

Given that the shapes are similar, the ratio of their areas is proportional to the square of the scale factor of their corresponding side lengths.

Here, the scale factor is 6. So to find the area ratio, we square the scale factor:
[tex]\[ \text{Area ratio} = 6^2 = 36 \][/tex]

Thus, the area of pentagon ABCDE is 36 times the area of pentagon PQRST.

From the given statements, the correct answer is:
C. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.