Question

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The length of a rectangular garden is 5 feet longer than it's width. The garden is surrounded by a 2 foot wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.

Answer 1

`Answer: \\ Let \: x \: be \: the \: length \: and \: y \: be \: the \: width \: of \: the \: garden \\ According \: to \: the \: problem \: we \: have \: a \: system: \\x - y = 5 \: \vee \: (x + 2)(y + 2) - xy = 76 \\ \Leftrightarrow \: x = (41)/(2) = 20.5 \: \vee \: y = (31)/(2) = 15.5 \\ So \: the \: length:20.5, width:15.5`

Answer 2

Width is 5 ft, length is 10ft.

Plug in the information given from the problem, in which the width is x, and the length is x + 5.

x(x+5) = x^2 + 5x

(x+4)(x+9) = x^2 + 13x +36

x^2 + 13x +36 - (x^2 + 5x) = 76

Simplify and result in 8x = 40

x = 5, which makes the length 10.