Question

A rectangular garden has a length that is six feet more than twice its width. It takes 120 feet of fencing to completely enclose the garden's area.

Write an equation that could be used to find the width of the garden. Clearly define your variable.

Explain how your equation models the given information.

Find the length of the garden algebraically. Show how you arrived at your answer.

Answer 1

Step-by-step explanation:

let width = w then length, l = 2w + 6

$2w + 2(2w + 6) = 120$

a rectangular garden has two pairs of equal parallel sides 2w and 2l. here we multiply 2 by the width and 2 by the length which is given as 6 more than twice the width or 2w + 6. we then add these sides to get 120

$2w + 2(2w + 6) = 120 \\ 2w + 4w + 12 = 120 \\ 6w + 12 = 120 \\ 6w + 12 - 12 = 120 - 12 \\ 6w = 108 \\ \frac{6w}{6} = \frac{108}{6 } \\ w = 18$

check

$width = w = 18\\ length \: l = 2w + 6 = 2(18) + 6 = 42\\ w + w + l + l = 120\\ 2w + 2l = \\ 2(18) + 2(42) = \\ 36 + 84 = 120$