Area of the rectangular lawn = 24 x 32 = 768 ft²
Given that the area of the remaining lawn = 425 ft²
Area of the walkway = 768 - 425 = 323 ft²
Let the width of the walkway be x.
Area of walkway = 2(32x) + 2(24x) - 4(x)² = 64x + 48x - 4x² = 112x - 4x²
112x - 4x² = 232
4x² - 112x + 232 = 0
(2x - 49) (2x - 7) = 0
x = 49/2 or x = 7/2
x = 24.5 (rejected, it cannot be bigger than the width) or x = 3.5
Answer: The width of the walkway is 3.5 feet.
