Width of Original Garden Question

In a rectangular garden, the length of the garden is twice its width. If the width of the garden is decreased by 4 meters, the new dimensions create a new rectangular area that is 32 square meters smaller than the original area. What is the width of the original garden?

Let the width of the original garden be denoted as $w$. Then the length can be expressed as $2w$. The area of the original garden is given by:

$$A = w imes 2w = 2w^2$$

When the width is decreased by 4 meters, the new width becomes $w - 4$ and the new length remains $2w$. Thus, the area of the new garden is:

$$A_{new} = (w - 4) imes (2w) = 2w^2 - 8w$$

According to the problem statement, the new area is 32 square meters smaller than the original area, leading to the equation:

$$A_{new} = A - 32$$

Substituting the equations for area gives us:

$$2w^2 - 8w = 2w^2 - 32$$

From here, solve for $w$.