Given the perimeter and length of the garden, the width of the garden was extended by 4 feet
Perimeter = 2(length+ width)
46 = 2{12 + (7 + w)}
46 = 2(12 + 7 + w)
46 = 2(19 + w)
46 = 38 + 2w
46 - 38 = 2w
8 = 2w
w = 8/2
w = 4 feet
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