# A rectangular garden, 42 feet by 20 feet, is surrounded by a walkway of uniform width. If the total area of the garden and walkway is 1248 square feet, What is the width of the walkway?

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by Topeng

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by Topeng

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Length of the garden + walkway = 42 + x

Width of the garden + walkway = 20 + x

Area of the garden including walkway = 1,248 ft²

Area = (L) (W)

1,248 = (42+x)(20+x)

1,248 = x² + 62x + 840

x² + 62x + 840 - 1248 = 0

x²+ 62x - 408 = 0

Factor: (x + 68) (x - 6) = 0

x + 68 = 0 x - 6 = 0

x = - 68

Choose the positive root, x = 6

To check:

(42 + 6 ft.) ( 20 + 6 ft.) = 1,248 ft²

(48 ft.) (26 ft.) = 1,248 ft²

1,248 ft² = 1,248 ft²