Question

The length of a rectangular garden is 8 feet longer than its width. The garden's perimeter is 188 feet. Find the width of the garden.

Answer 1

44 Feet

Explanation:

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Answer 2

Width = 43 feet

Explanation:

Given the 188-feet perimeter of a rectangular garden, for which its length is 8 feet longer than its width:

We can express the length of the rectangular garden as: 8 + W.

Hence, in order to solve for the length and the width of the rectangular garden, use the following formula for the perimeter of a rectangle:

Perimeter (P) = 2(L + W) or 2L + 2W = 188 feet

Length (L) = 8 + W

Width (W) = W

Substitute these values into the perimeter formula to solve for the value of the rectangular garden's dimensions:

P = 2L + 2W

188 feet = 2(8 + W) + 2W

Distribute 2 into the parenthesis, (8 + W):

188 = 16 + 2W + 2W

Combine like terms:

188 = 16 + 4W

Subtract 16 from both sides:

188 - 16 = 16 - 16 + 4W

172 = 4W

Divide both sides by 4 to solve for W:

`\LARGE\mathsf{(172)/(4)\:=\:(4W)/(4)}`

W = 43

Therefore, the width of a rectangular garden is 43 feet.

Since we determined that the length is 8 + W, then it means that the length of the rectangular garden is 51 feet.

Verify the dimensions:

Double-check whether we have the correct dimensions for the rectangular garden by substituting the length (L) = 51 feet, and the width (W) = 43 feet, into the perimeter formula:

P = 2L + 2W

188 feet = 2(51) + 2(43)

188 feet = 102 + 86

188 feet = 188 feet (True statement). This means that we have the correct dimensions for the rectangular garden.

Answers:

Therefore, the width of a rectangular garden is 43 feet.