A rectangular garden has a length that is twice its width. If the area of the garden can be represented by the equation \( A = x(2x) \), where \( x \) is the width in meters, what are the dimensions of the garden when the area is 50 square meters?

To find the dimensions of the garden, we start with the given area equation \( A = x(2x) \), which simplifies to \( A = 2x^2 \). We can set this equal to 50 square meters: \[ 2x^2 = 50 \] Dividing both sides by 2 gives us: \[ x^2 = 25 \] Taking the square root of both sides, we find: \[ x = 5 \] Now that we have the width \( x = 5 \) meters, we can find the length. Since the length is twice the width: \[ \text{Length} = 2x = 2(5) = 10 \text{ meters} \] Thus, the dimensions of the garden are: - Width: 5 meters - Length: 10 meters It’s a perfect setup for gardening—just make sure to plant your favorite flowers or veggies!