Question

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 240 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.

Find the length and width.

Answer 1

• length: 72 feet
• width: 48 feet

Explanation:

The sum of length and width is half the perimeter, 120 feet. Since the ratio of length to width is 3 : 2, the length is 3/(3+2) = 3/5 of the sum of length and width.

length = 3/5 × 120 ft = 72 ft

width = 2/3 length = 2/3 × 72 ft = 48 ft

The length and width of the garden are 72 feet and 48 feet, respectively.

Answer 2

Answer: length = 72 feet

Width = 48 feet

Explanation:

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

The width is exactly two-thirds of the length. It means that

W = 2L/3

If 240 feet of antique picket fencing are to be used to enclose the garden, it means that the perimeter of the rectangular field is 240 feet. The perimeter of the rectangular field is expressed as

2(L+W). Therefore,

2( L+ W) = 240

L+ B = 120

Substituting W = 2L/3 into L+ B = 120, it becomes

L + 2L/3 = 120

3L + 2L = 360

5L = 360

L = 360/5 = 72 feet

W = 2L/3

W = 2×72/3 = 144/3

W = 48 feet