The dimensions of Mrs. Singleton's square garden are dilated using a scale factor of 3. What is the relationship between the area of the new garden and the old garden?
A. The are of the new garden is nine times the area of the original garden
B. The area of the new garden is 1/2 of the area of the original garden
C. The are of the new garden is 1/3 of the area of the original garden
D. The area of the new garden is three times the area of the original garden
area goes up as the dilation squared, so (A)
The enswer is 15
To find the relationship between the area of the new garden and the old garden after dilating the dimensions using a scale factor of 3, we need to consider the effect of the scale factor on the area.
When the dimensions of a shape are dilated using a scale factor of k, the area of the dilated shape is multiplied by k^2.
In this case, the scale factor is 3, so the area of the new garden will be multiplied by 3^2 = 9.
Therefore, the correct answer is:
A. The area of the new garden is nine times the area of the original garden