Final answer:
The width of the garden is found by solving the equation 50 = 5w, resulting from the perimeter formula (P = 2l + 2w) with l set to 1.5 times the width (w). The width is 10 feet.
Step-by-step explanation:
To find the width of the garden, we can set up an equation using the perimeter formula of a rectangle (P = 2l + 2w) and the given information that the length (l) is 1.5 times the width (w). Since the perimeter (P) is 50 feet:
P = 2l + 2w = 50 feet,
l = 1.5w.
Substitute the expression for l into the perimeter equation:
50 = 2(1.5w) + 2w,
50 = 3w + 2w,
Combine the terms:
50 = 5w,
Solve for the width (w):
w = 50 / 5,
w = 10 feet.
Therefore, the width of the garden is 10 feet.