Answer:
length = 40 ft; width = 8 ft
Step-by-step explanation:
Let the width = x.
The fence has to go around the entire perimeter of the garden.
A rectangle has 4 sides: 2 lengths and 2 widths.
The perimeter is the sum of the lengths of the 4 sides.
perimeter = length + length + width + width
We are told the perimeter is 96 ft, so we have:
length + length + width + width = 96
Above, we let the width = x.
The length of the rectangle is 16 ft more than 3 times the width.
Since the width is x, the length is 3 times the width, 3x, plus 16, so the width is 3x + 16. We substitute x for each width and 3x + 16 for each length.
length + length + width + width = 96
3x + 16 + 3x + 16 + x + x = 96
Add like terms on the left side.
3x + 3x + x + x + 16 + 16 = 96
8x + 32 = 96
Subtract 32 from both sides.
8x = 64
Divide both sides by 8.
x = 8
Since we let the width = x, now we know the width is 8 ft.
The length is 16 ft more than 3 times the width.
length = 3x + 16 = 3(8) + 16 = 24 + 16 = 40
Answer: length = 40 ft; width = 8 ft
Check: 40 ft is indeed 16 more than 3 times 8 since 3(8) + 16 = 40.
Also, 2 lengths of 40 ft and 2 widths of 8 ft do add to 96 ft.
Our answer is correct.
