Answer: the area of the garden is 493 ft²
Step-by-step explanation:
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
If he has 92 feet of fencing, it means that
2(L + W) = 92
Dividing through by 2, it becomes
L + W = 46 - - - - - - - - - - - -1
He wants the length of the garden to be five feet less than twice its width. This means that
L = 2W - 5
Substituting L = 2W - 5 into equation 1, it becomes
2W - 5 + W = 46
2W + W = 46 + 5
3W = 51
W = 51/3
W = 17 feet
L = 2W - 5 = 2 × 17 - 5
L = 29 feet
The area of the garden is
LW = 29 × 17 = 493 ft²
