Question

a rectangular garden has length twice as great as its width. a second rectangular garden has the same length as the first garden and width that is 4 meters greater than the width of the first garden. the second garden has area of 120 square meters. what is the length of the two gardens? enter your answer in the box.

Explanation:

Step1: Define variables for first garden

Let width of first garden = $w$. Then length = $2w$.

Step2: Define second garden dimensions

Length of second garden = $2w$, width = $w + 4$.

Step3: Set up area equation

Area of second garden: $2w(w + 4) = 120$
Simplify: $2w^2 + 8w = 120$
Divide by 2: $w^2 + 4w - 60 = 0$

Step4: Solve quadratic equation

Factor: $(w + 10)(w - 6) = 0$
Solutions: $w = -10$ (discard, invalid width) or $w = 6$

Step5: Calculate length

Length = $2w = 2\times6 = 12$

Answer:

12 meters