Question
Problem 13) Suppose we have a rectangle with an area of A = 21= (7*3) (pictured below). If we dilate this rectangle by a linear scale factor of k = 2, what will be the new area?
Answers
GPT-4o mini
When a rectangle is dilated by a linear scale factor \( k \), the new area can be determined using the square of that scale factor.
The original area of the rectangle is given as \( A = 21 \).
When we dilate the rectangle by a scale factor \( k = 2 \), the new area \( A' \) can be calculated using the formula:
\[
A' = k^2 \cdot A
\]
Substituting the values we have:
\[
A' = 2^2 \cdot 21 = 4 \cdot 21 = 84
\]
Thus, the new area after dilation is \( \boxed{84} \).
The original area of the rectangle is given as \( A = 21 \).
When we dilate the rectangle by a scale factor \( k = 2 \), the new area \( A' \) can be calculated using the formula:
\[
A' = k^2 \cdot A
\]
Substituting the values we have:
\[
A' = 2^2 \cdot 21 = 4 \cdot 21 = 84
\]
Thus, the new area after dilation is \( \boxed{84} \).