Question

A garden is in the shape of a square with a perimeter of 64 feet. The garden is surrounded by two

fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from the
first fence on the outside. If the material used to build the two fences is $1.26 per foot, what was the
total cost of the fences?

Answer 1

The perimeter of a square is the sum of its sides and they are all equal, so to obtain the length of each of them we divide the perimeter of the first fence between 4:

`\text{P1}= \frac{\text{64 feet}}{\text{4 sides}}`

`\text{P1}= 16 \ \text{feet}`

Then, the length of each side of the second fence will increase 2 feet at each end, as shown in the figure. We have then that the perimeter of the second fence is:

`\text{P2 = 20 feet} * \text{4 sides}`

`\text{P2 = 80 feet}`

The sum of the perimeters of both fences is:

`\text{PT = P1 + P2}`

`\text{PT = 64 feet + 80 feet}`

`\text{PT = 144 feet}`

Total cost = $1.26 x 144 feet

Total cost = $181.44

The total cost of the fences was $181.44