A garden has the shape of a rectangle.
This garden is enlarged to create a new garden.
Its width is doubled and its length is tripled.
How many times larger is the area of the new garden than the area of the old garden?
\(\boxed{6}\) times larger is the area of the new garden than the area of the old garden.
Step 1 :Let the width of the old garden be W and the length be L.
Step 2 :The width of the new garden is doubled, so it is 2W.
Step 3 :The length of the new garden is tripled, so it is 3L.
Step 4 :The area of the old garden is \(A_{old} = W \times L\).
Step 5 :The area of the new garden is \(A_{new} = (2W) \times (3L) = 6WL\).
Step 6 :The ratio of the area of the new garden to the area of the old garden is \(\frac{A_{new}}{A_{old}} = \frac{6WL}{WL} = 6\).
Step 7 :\(\boxed{6}\) times larger is the area of the new garden than the area of the old garden.