Question
Problem 12) Suppose we have these two similar squares that are related by a scale factor of k = 4. What is the ratio of their areas? (hint: ratio = bigger square/smaller square)
for square ABCD their lengths are all the same and are each 4.
for square PQRS their lengths are also all the same and are each 16.
the multiple choice answers go as follows:
Ratio = 3
Ratio = 3
Ratio = 12
Ratio = 12
Ratio = 16
Ratio = 16
Ratio = 10
for square ABCD their lengths are all the same and are each 4.
for square PQRS their lengths are also all the same and are each 16.
the multiple choice answers go as follows:
Ratio = 3
Ratio = 3
Ratio = 12
Ratio = 12
Ratio = 16
Ratio = 16
Ratio = 10
Answers
GPT-4o mini
To find the ratio of the areas of the two squares, we can use the fact that if two similar figures have a scale factor of \( k \), then the ratio of their areas is given by \( k^2 \).
Given:
- The scale factor \( k = 4 \).
Now, we calculate the ratio of the areas:
\[
\text{Ratio of areas} = k^2 = 4^2 = 16.
\]
So the ratio of the areas of the larger square to the smaller square is \( 16 \).
The correct answer is:
**Ratio = 16**.
Given:
- The scale factor \( k = 4 \).
Now, we calculate the ratio of the areas:
\[
\text{Ratio of areas} = k^2 = 4^2 = 16.
\]
So the ratio of the areas of the larger square to the smaller square is \( 16 \).
The correct answer is:
**Ratio = 16**.