To determine the linear scale factor of two similar shapes given that their area factor is 49:121, follow these steps:
1. Understand the relationship between area factor and linear scale factor:
- When two shapes are similar, their areas are proportional to the square of the linear scale factor. This means if the area ratio is [tex]\( \frac{A_1}{A_2} \)[/tex], then the linear scale factor ratio is the square root of [tex]\( \frac{A_1}{A_2} \)[/tex].
2. Given area factor ratio:
- The area factor is given as [tex]\( \frac{49}{121} \)[/tex].
3. Calculate the linear scale factor:
- The linear scale factor is the square root of the area factor. Thus, you take the square root of both the numerator and the denominator of the area factor.
4. Square root of the numerator:
- The square root of 49 is [tex]\( 7 \)[/tex].
5. Square root of the denominator:
- The square root of 121 is [tex]\( 11 \)[/tex].
6. Form the linear scale factor ratio:
- Therefore, the linear scale factor ratio is [tex]\( 7 : 11 \)[/tex].
So the correct linear scale factor given an area factor of 49:121 is:
[tex]\[ \boxed{7 : 11} \][/tex]
Hence, the correct answer is C. 7 : 11.
