To solve this problem, you simply apply the scale factor to both dimensions (length and width) of the original rectangle and then calculate the area of the new rectangle.
The original area of the rectangle is 52 square yards. If both the length and width are multiplied by 15, both dimensions increase by a factor of 15.
To find the new area, we must square the multiplication factor because the area is a two-dimensional measure (length times width), and since both dimensions are multiplied by the same factor, the new area will be the original area multiplied by the square of the factor.
The multiplication factor squared is:
\( 15^2 = 225 \)
Now, to find the new area, we multiply the original area by this scale factor squared:
New area = Original area \( \times \) Scale factor squared
New area = \( 52 \) square yards \( \times \ 225 \)
New area = \( 11,700 \) square yards
So the area of the new rectangle is 11,700 square yards.
The correct answer is C) 11,700 yd².